In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup...In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.展开更多
Let A and B be unital Banach algebra and M be Banach A, B-module. Then T＇ = （AB^M） becomes a triangular Banach algebra when equipped with the Banach space norm ｜｜（ ab^m）｜｜ = ｜｜a｜｜A ＋｜｜m｜｜M ＋ ｜｜b｜...Let A and B be unital Banach algebra and M be Banach A, B-module. Then T＇ = （AB^M） becomes a triangular Banach algebra when equipped with the Banach space norm ｜｜（ ab^m）｜｜ = ｜｜a｜｜A ＋｜｜m｜｜M ＋ ｜｜b｜｜m A Banach algebra T is said to be Lie n-weakly amenable if all Lie derivations from T into its nth dual space T^（n） are standard. In this paper we investigate Lie n-weak amenability of a triangular Banach algebra T in relation to that of the algebras A, B and their action on the module M.展开更多
Let G be a locally compact group, H a closed amenable subgroup and u an element of the Herz Figà-Talamanca algebra of H with compact support, we prove the existence of an extension of u to G, with a good control ...Let G be a locally compact group, H a closed amenable subgroup and u an element of the Herz Figà-Talamanca algebra of H with compact support, we prove the existence of an extension of u to G, with a good control of the norm and of the support of the extension.展开更多
Let A and B be Banach algebras and T ： B → A be a continuous homomorphism, n- weak amenability of the Banach algebra A ：X：T B （defined in Bade, W. G., Curtis, P. C., Dales, H. G.： Amenability and weak amenabilit...Let A and B be Banach algebras and T ： B → A be a continuous homomorphism, n- weak amenability of the Banach algebra A ：X：T B （defined in Bade, W. G., Curtis, P. C., Dales, H. G.： Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc., 55（2）, 359-377 （1987）） is studied. The new version of a Banach algebra defined with a continuous homomorphism is introduced and Arens regularity and various notions of amenability of this algebra are studied.展开更多
In this paper, the concepts of approximate character amenability （contractibility）, uniform approximate character amenability （contractibility） and w^＊-approximate character amenability are introduced. We are con...In this paper, the concepts of approximate character amenability （contractibility）, uniform approximate character amenability （contractibility） and w^＊-approximate character amenability are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebras. We show that approximate character amenability, w^＊-approximate character amenability and approximate character contractibility are the same properties, as uniform approximate character amenability and character amenability as uniform approximate character contractibility and character contractibility. The general theory for these concepts is also developed. Moreover, approximate character amenability of several concrete classes of Banach algebras related to locally compact groups and also some discrete semigroups is considered.展开更多
In this paper,we study the Bowen entropy of stable sets in positive entropy G-system of amenable group actions.The lower bound of the Bowen entropy of these sets are estimated.
For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A =...For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A = G<sub>αγ</sub><sup>×</sup> A, if G is amenable. About the inverse, few discussions have been seen.展开更多
Exploring the creation of comfortable objects in traditional tourism villages from the perspective of tourists can help reveal the essence of these amenities.Taking Yidoushui Ancient Village in Jiaozuo City,Henan Prov...Exploring the creation of comfortable objects in traditional tourism villages from the perspective of tourists can help reveal the essence of these amenities.Taking Yidoushui Ancient Village in Jiaozuo City,Henan Province as an example,this study applied the five-element theory of rural amenities to the research on the tourism-oriented traditional villages.With the help of text analysis tools and field investigations,it identified the objects,indicators,and elements of amenities in Yidoushui Ancient Village.Based on this framework,a survey questionnaire was designed for field research,followed by data analysis.The results indicated that tourists primarily focused on ecological amenities in traditional tourism villages;overall,visitors exhibited relative high perception and positive evaluation of the amenities;there were significant differences in the impact of different amenities indicators on tourist experience,and multiple indicators of ecological amenities showed significantly positive correlation with tourists’mood,satisfaction,and revisit intention,making them core factors in enhancing tourist experience.Cultural amenities significantly improved mood and satisfaction,but showed no significant effect on revisit intention.展开更多
In this paper,we study the properties of the scaled packing topological pressures for a topological dynamical system(X,G),where G is a countable discrete infinite amenable group.We show that the scaled packing topolog...In this paper,we study the properties of the scaled packing topological pressures for a topological dynamical system(X,G),where G is a countable discrete infinite amenable group.We show that the scaled packing topological pressures can be determined by the scaled Bowen topological pressures.We obtain Billingsley’s Theorem for the scaled packing pressures with a G-action.Then we get a variational principle between the scaled packing pressures and the scaled measure-theoretic upper local pressures.Finally,we give some restrictions on the scaled sequence b,then in the case of the set Xμof generic points,we prove thatP^(P)(X_(μ),{F_(n)},f,b)=h_(μ)(X)+∫_(X)∫dμ,if(F(n))is tempered andμis a G-invariant ergodic Borel probability measure.展开更多
Adequate,safe and affordable housing and basic services for all are the basis for sustainable development,livelihood security and basic housing rights.Shelter is a basic human rights guarantee and improvements in livi...Adequate,safe and affordable housing and basic services for all are the basis for sustainable development,livelihood security and basic housing rights.Shelter is a basic human rights guarantee and improvements in living conditions are of significant importance to the quality of life.The article uses data from China’s fifth,sixth and seventh population censuses to reveal the spatial and temporal differences in the improvement of housing conditions of households in 281 cities in China from 2000 to 2020.The study concludes the following:(i)The housing conditions score of urban households in China has improved significantly,and the living environment has been significantly improved.The center of gravity of the overall housing conditions score shifts from the western region to the eastern region and then to the central region.(ii)The housing facilities in China’s cities have become increasingly sophisticated during the study period.The overall variation in housing amenities tends to decrease overall,with higher intra-belt variation than inter-belt variation in the four main regions.(iii)Self-built housing,rented housing,purchased housing,other types of housing and inherited housing are the main sources of housing for urban househ olds in China.From 2000 to 2020,the housing structure is characterized by two increases and one decrease,namely an increase in the proportion of purchased and rented housing and a decrease in the proportion of self-built housing.(iv)The main factors influencing the improvement of housing conditions are historical factors,the forces of marketization,urbanization,and housing policy.展开更多
Any covering Y→X of a hyperbolic Riemann surface X determines an inclusion of Teichmuller spaces T(X)→T(Y). This map is shown to be an isometry for the Teichmuller metric iff the covering is amenable, and contractin...Any covering Y→X of a hyperbolic Riemann surface X determines an inclusion of Teichmuller spaces T(X)→T(Y). This map is shown to be an isometry for the Teichmuller metric iff the covering is amenable, and contracting iff for any [μ]εT(X), where is the Poincare series operator. Furthermore the inclusion is not a uniform contraction on T(X).展开更多
Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenabilit...Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenability and inner amenability for locally compact groups. In this paper, among other things, we extend some standard results for amenable groups to F-amenable groups and give various characterizations for F-amenable groups. A sequence of characterizations of F-amenable groups is given here by developing the well-known Flner＇s conditions for amenable locally compact groups. Several characterizations of inner amenability are also given.展开更多
Several equivalent formulations are given for equivariant coarse embedding into Hilbert space.Using these equivalent definitions,it is proved that for a metric space X and a Hilbert space H with proper and isometric g...Several equivalent formulations are given for equivariant coarse embedding into Hilbert space.Using these equivalent definitions,it is proved that for a metric space X and a Hilbert space H with proper and isometric group actions on both of them,if X is coarsely embeddable into H and the group is amenable,then the coarse embedding can be modified to be equivariant by using the invariant mean property of the amenable group.展开更多
Based on road characters in Jiangnan New District in Mudanjiang Municipality,four typical roads were selected to carry out road afforestation design with consideration of local building features and local vegetations,...Based on road characters in Jiangnan New District in Mudanjiang Municipality,four typical roads were selected to carry out road afforestation design with consideration of local building features and local vegetations,in order to integrate both of landscape effects,in terms of improving and beautifying city environment,and of ecological effects,such as filtering air,reducing temperature,increasing humidity,and reducing noise.展开更多
文摘In this article, the approximate amenability of semigroup algebra e1（S） is investigated, where S is a uniformly locally finite inverse semigroup. Indeed, we show that for a uniformly locally finite inverse semigroup S, the notions of amenability, approximate amenability and bounded approximate amenability of e1（S） are equivalent. We use this to give a direct proof of the approximate amenability of e1 （S） for a Brandt semigroup S. Moreover, we characterize the approximate amenability of e1（S）, where S is a uniformly locally finite band semigroup.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117124411601010)
文摘Let A and B be unital Banach algebra and M be Banach A, B-module. Then T＇ = （AB^M） becomes a triangular Banach algebra when equipped with the Banach space norm ｜｜（ ab^m）｜｜ = ｜｜a｜｜A ＋｜｜m｜｜M ＋ ｜｜b｜｜m A Banach algebra T is said to be Lie n-weakly amenable if all Lie derivations from T into its nth dual space T^（n） are standard. In this paper we investigate Lie n-weak amenability of a triangular Banach algebra T in relation to that of the algebras A, B and their action on the module M.
文摘Let G be a locally compact group, H a closed amenable subgroup and u an element of the Herz Figà-Talamanca algebra of H with compact support, we prove the existence of an extension of u to G, with a good control of the norm and of the support of the extension.
基金UGC for UGC-SAP-DRS-Ⅱ(Grant No.F.510/3/DRS/2009)provided to the Department of Mathematics,Sardar Patel University,Vallabh Vidyanagar-388120,India
文摘Let A and B be Banach algebras and T ： B → A be a continuous homomorphism, n- weak amenability of the Banach algebra A ：X：T B （defined in Bade, W. G., Curtis, P. C., Dales, H. G.： Amenability and weak amenability for Beurling and Lipschitz algebras. Proc. London Math. Soc., 55（2）, 359-377 （1987）） is studied. The new version of a Banach algebra defined with a continuous homomorphism is introduced and Arens regularity and various notions of amenability of this algebra are studied.
基金supported by National Natural Science Foundation of China (Grant No. 11226125)
文摘In this paper, the concepts of approximate character amenability （contractibility）, uniform approximate character amenability （contractibility） and w^＊-approximate character amenability are introduced. We are concerned with the relations among the generalized concepts of character amenability for Banach algebras. We show that approximate character amenability, w^＊-approximate character amenability and approximate character contractibility are the same properties, as uniform approximate character amenability and character amenability as uniform approximate character contractibility and character contractibility. The general theory for these concepts is also developed. Moreover, approximate character amenability of several concrete classes of Banach algebras related to locally compact groups and also some discrete semigroups is considered.
基金Supported by NSFC(No.11861010),also supported by NSFC(No.12171175),also supported by NSFC(No.12261006)NSF of Guangxi Province(No.2018GXNSFFA281008)Project of Guangxi First Class Disciplines of Statistics(No.GJKY-2022-01)。
文摘In this paper,we study the Bowen entropy of stable sets in positive entropy G-system of amenable group actions.The lower bound of the Bowen entropy of these sets are estimated.
文摘For convenience, all notations and terminologies are referred to Ref. [1]. It is well known that for a C<sup>*</sup>-dynamic system （A, G, α）, G<sub>α</sub><sup>×</sup> A = G<sub>αγ</sub><sup>×</sup> A, if G is amenable. About the inverse, few discussions have been seen.
基金Sponsored by Humanities and Social Sciences Research Planning Fund of the Ministry of Education of China(23YJAZH171)Philosophy and Social Sciences Project of Henan Province,China(2024XWH099).
文摘Exploring the creation of comfortable objects in traditional tourism villages from the perspective of tourists can help reveal the essence of these amenities.Taking Yidoushui Ancient Village in Jiaozuo City,Henan Province as an example,this study applied the five-element theory of rural amenities to the research on the tourism-oriented traditional villages.With the help of text analysis tools and field investigations,it identified the objects,indicators,and elements of amenities in Yidoushui Ancient Village.Based on this framework,a survey questionnaire was designed for field research,followed by data analysis.The results indicated that tourists primarily focused on ecological amenities in traditional tourism villages;overall,visitors exhibited relative high perception and positive evaluation of the amenities;there were significant differences in the impact of different amenities indicators on tourist experience,and multiple indicators of ecological amenities showed significantly positive correlation with tourists’mood,satisfaction,and revisit intention,making them core factors in enhancing tourist experience.Cultural amenities significantly improved mood and satisfaction,but showed no significant effect on revisit intention.
基金supported by the NNSF of China(12201120)the visiting fellowships supported by Fujian Alliance of Mathematics while visiting Xiamen University in the winter of 2023。
文摘In this paper,we study the properties of the scaled packing topological pressures for a topological dynamical system(X,G),where G is a countable discrete infinite amenable group.We show that the scaled packing topological pressures can be determined by the scaled Bowen topological pressures.We obtain Billingsley’s Theorem for the scaled packing pressures with a G-action.Then we get a variational principle between the scaled packing pressures and the scaled measure-theoretic upper local pressures.Finally,we give some restrictions on the scaled sequence b,then in the case of the set Xμof generic points,we prove thatP^(P)(X_(μ),{F_(n)},f,b)=h_(μ)(X)+∫_(X)∫dμ,if(F(n))is tempered andμis a G-invariant ergodic Borel probability measure.
基金Project of Philosophy and Social Science of Shanghai“Study on the Role of Population Ageing on Economic Growth in the Yangtze River Delta Urban Agglomeration”(2023ZSH002).
文摘Adequate,safe and affordable housing and basic services for all are the basis for sustainable development,livelihood security and basic housing rights.Shelter is a basic human rights guarantee and improvements in living conditions are of significant importance to the quality of life.The article uses data from China’s fifth,sixth and seventh population censuses to reveal the spatial and temporal differences in the improvement of housing conditions of households in 281 cities in China from 2000 to 2020.The study concludes the following:(i)The housing conditions score of urban households in China has improved significantly,and the living environment has been significantly improved.The center of gravity of the overall housing conditions score shifts from the western region to the eastern region and then to the central region.(ii)The housing facilities in China’s cities have become increasingly sophisticated during the study period.The overall variation in housing amenities tends to decrease overall,with higher intra-belt variation than inter-belt variation in the four main regions.(iii)Self-built housing,rented housing,purchased housing,other types of housing and inherited housing are the main sources of housing for urban househ olds in China.From 2000 to 2020,the housing structure is characterized by two increases and one decrease,namely an increase in the proportion of purchased and rented housing and a decrease in the proportion of self-built housing.(iv)The main factors influencing the improvement of housing conditions are historical factors,the forces of marketization,urbanization,and housing policy.
文摘Any covering Y→X of a hyperbolic Riemann surface X determines an inclusion of Teichmuller spaces T(X)→T(Y). This map is shown to be an isometry for the Teichmuller metric iff the covering is amenable, and contracting iff for any [μ]εT(X), where is the Poincare series operator. Furthermore the inclusion is not a uniform contraction on T(X).
文摘Let G be a locally compact group and let F be a closed subgroup of G × G. Pier introduced the notion of F-amenability which gives a new classification of groups. This concept generalizes the concept of amenability and inner amenability for locally compact groups. In this paper, among other things, we extend some standard results for amenable groups to F-amenable groups and give various characterizations for F-amenable groups. A sequence of characterizations of F-amenable groups is given here by developing the well-known Flner＇s conditions for amenable locally compact groups. Several characterizations of inner amenability are also given.
基金Supported by National Natural Science Foundation of China(11871342)。
文摘Several equivalent formulations are given for equivariant coarse embedding into Hilbert space.Using these equivalent definitions,it is proved that for a metric space X and a Hilbert space H with proper and isometric group actions on both of them,if X is coarsely embeddable into H and the group is amenable,then the coarse embedding can be modified to be equivariant by using the invariant mean property of the amenable group.
基金Supported by Special Project for Teaching Reform of Mudanjiang Normal University(2013JGZX0072)Project for Teaching Reform of Mudanjiang Normal University(2013ALZX019)+1 种基金Training Program of Mudanjiang Normal UniversityHorizontal Topic of Mudanjiang Normal University(KH0472)~~
文摘Based on road characters in Jiangnan New District in Mudanjiang Municipality,four typical roads were selected to carry out road afforestation design with consideration of local building features and local vegetations,in order to integrate both of landscape effects,in terms of improving and beautifying city environment,and of ecological effects,such as filtering air,reducing temperature,increasing humidity,and reducing noise.
