In this paper we study the isomorphisms of two ＊-bisimple type A ω2-semigroups such that D^＊ = ^~D） and obtain a criterion for isomorphisms of two such semigroups.
In this paper, we apply the contraction mapping theorem to establish some bounded and unbounded additive perturbation theorems concerning local C-semigroups. Some growth conditions of perturbations of local C-semigrou...In this paper, we apply the contraction mapping theorem to establish some bounded and unbounded additive perturbation theorems concerning local C-semigroups. Some growth conditions of perturbations of local C-semigroups axe also established.展开更多
We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some...We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some additive perturbation results concerning S（·）. Some growth conditions of the perturbations of S（·） are also established.展开更多
Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigrou...Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.展开更多
This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X, First, the sufficient and necessary conditions for a local C-se...This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X, First, the sufficient and necessary conditions for a local C-semigroup and a C-cosine function to be the restriction of a global C-semigroup and a global C-cosine function to an interval are given, respectively, Secondly, it is characterized for a closed operator to be the generator of a local C-semigroup and a local C-cosine function, respectively.展开更多
In this paper, the existence, uniqueness, and asymptotic behavior of the solution of the density evolution equation for M/M/∞ model was studied by the semigroup theory of linear operators.
In this paper, we study ＊-simple type A ω2 -semigroups in which D＊= D and D＊｜ES = Md by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two ...In this paper, we study ＊-simple type A ω2 -semigroups in which D＊= D and D＊｜ES = Md by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two such semigroups.展开更多
In this paper,we study the complex symmetric C_(0)-semigroups of weighted composition operators W_(ψ,φ)on the weighted Hardy spaces H_(γ) of the unit disk D.It is well-known that there are only two classes of weigh...In this paper,we study the complex symmetric C_(0)-semigroups of weighted composition operators W_(ψ,φ)on the weighted Hardy spaces H_(γ) of the unit disk D.It is well-known that there are only two classes of weighted composition conjugations A_(u,v) on H_(γ)(D):either C_(1) or C_(2).We completely characterize C_(1)-symmetric(C_(2)-symmetric)C_(0)-semigroups of weighted composition operators W_(ψ,φ) on H_(γ)(D).展开更多
It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend...It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.展开更多
By means of Riemann-Stieltjes stochastic process, moment-generating functions and operator-valued mathematical expectation, the problem of probabilistic approximation for bi-continuous C-semigroups is studied and the ...By means of Riemann-Stieltjes stochastic process, moment-generating functions and operator-valued mathematical expectation, the problem of probabilistic approximation for bi-continuous C-semigroups is studied and the general probabilistic approximation of exponential formulas and the generation theorems are given.展开更多
The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
In this paper, we define the concept of general C semigroup, which is an generalization of C semigroup. The generator and the genertion of this general C semigroup are discussed. Some examples and inter...In this paper, we define the concept of general C semigroup, which is an generalization of C semigroup. The generator and the genertion of this general C semigroup are discussed. Some examples and interesting applications are given too.展开更多
In this paper, we introduce the definition of （m, n）0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green＇s relations. Extending and generalizing the Croi...In this paper, we introduce the definition of （m, n）0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green＇s relations. Extending and generalizing the Croisot＇s Theory of Decomposition for F-semigroups, we introduce and study the absorbent and regular absorbent Г-semigroups. We approach this problem by examining quasi-ideals using Green＇s relations.展开更多
Left (right) C-semigroups are the regular semigroups satisfying the following condition:eSSe (SeeS) for every e∈E (the set of idempotents of S). Refs. [1, 2] give the left(right) semi-spined product structure and the...Left (right) C-semigroups are the regular semigroups satisfying the following condition:eSSe (SeeS) for every e∈E (the set of idempotents of S). Refs. [1, 2] give the left(right) semi-spined product structure and the left (right) △-product structure of a left(right) C-semigroup, respectively. It is easy to see that the above condition defining a reg-ular semigroup S to be a left (right) C-semigroup may be replaced by the following condi-tion:展开更多
The investigation of U-ample ω-semigroups is initiated. After obtaining some properties of such semigroups, a structure of U-ample ω-semigroups is established. It is proved that a semigroup is a U-ample ω-semigroup...The investigation of U-ample ω-semigroups is initiated. After obtaining some properties of such semigroups, a structure of U-ample ω-semigroups is established. It is proved that a semigroup is a U-ample ω-semigroup if and only if it can be expressed by WBR（T, 0）, namely, the weakly Bruck-Reilly extensions of a monoid T. This result not only extends and amplifies the structure theorem of bisimple inverse ω-semigroups given by N. R. Reilly, but also generalizes the structure theorem of ,-bisimple type A ω-semigroups given by U. Asibong-Ibe in 1985.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.10901134)the Science Foundation of the Department of Education of Yunnan Province(Grant No.2011Y478)
文摘In this paper we study the isomorphisms of two ＊-bisimple type A ω2-semigroups such that D^＊ = ^~D） and obtain a criterion for isomorphisms of two such semigroups.
基金supported by the National Science Council of Taiwan
文摘In this paper, we apply the contraction mapping theorem to establish some bounded and unbounded additive perturbation theorems concerning local C-semigroups. Some growth conditions of perturbations of local C-semigroups axe also established.
文摘We establish some left and right multiplicative perturbations of a local α-timesintegrated C-semigroup S（·） on a complex Banach space X with non-densely defined genera- tor, which can be applied to obtain some additive perturbation results concerning S（·）. Some growth conditions of the perturbations of S（·） are also established.
基金Leading Academic Discipline Project of SHNU,China (No.DZL803)Innovation Project of Shanghai Education Committee,China(No.12YZ081)+2 种基金General Scientific Research Project of SHNU,China (No.SK201121)National Natural Science Foundation of China(No.11001046)Fundamental Research Fundation for the Central Universities,China (No.11D10904)
文摘Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.
基金the National Natural Science Foundation of China,and the Natural Science Foundation of Shanxi Province and the Youth Scientific
文摘This paper is concerned with the local C-semigroups and local C-cosine functions without the assumption that the image of C is dense in a Banach space X, First, the sufficient and necessary conditions for a local C-semigroup and a C-cosine function to be the restriction of a global C-semigroup and a global C-cosine function to an interval are given, respectively, Secondly, it is characterized for a closed operator to be the generator of a local C-semigroup and a local C-cosine function, respectively.
文摘In this paper, the existence, uniqueness, and asymptotic behavior of the solution of the density evolution equation for M/M/∞ model was studied by the semigroup theory of linear operators.
基金The NSF (10901134) of Chinathe Science Foundation (2011Y478) of the Department of Education of Yunnan Province
文摘In this paper, we study ＊-simple type A ω2 -semigroups in which D＊= D and D＊｜ES = Md by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two such semigroups.
文摘In this paper,we study the complex symmetric C_(0)-semigroups of weighted composition operators W_(ψ,φ)on the weighted Hardy spaces H_(γ) of the unit disk D.It is well-known that there are only two classes of weighted composition conjugations A_(u,v) on H_(γ)(D):either C_(1) or C_(2).We completely characterize C_(1)-symmetric(C_(2)-symmetric)C_(0)-semigroups of weighted composition operators W_(ψ,φ) on H_(γ)(D).
基金Project of Sichuan Provincial Science and Technology Department (No.2007J13-006)
文摘It is proved that a system under compact perturbation cannot be uniformly exponentially stable for an isometric C0-semigroup or a C0-group with polynomial growth for negative time in a Banach space. The results extend and improve the corresponding results of previous literature.
基金The NSF(10671205)of ChinaFundamental Research Funds(3142012022,3142013039 and 3142014039)for the Central Universitiesthe Key Discipline Construction Project(HKXJZD201402)of NCIST
文摘By means of Riemann-Stieltjes stochastic process, moment-generating functions and operator-valued mathematical expectation, the problem of probabilistic approximation for bi-continuous C-semigroups is studied and the general probabilistic approximation of exponential formulas and the generation theorems are given.
文摘The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.
文摘In this paper, we define the concept of general C semigroup, which is an generalization of C semigroup. The generator and the genertion of this general C semigroup are discussed. Some examples and interesting applications are given too.
文摘In this paper, we introduce the definition of （m, n）0-regularity in Г-semigroups. we in- vestigate and characterize the 20-regular class of F-semigroups using Green＇s relations. Extending and generalizing the Croisot＇s Theory of Decomposition for F-semigroups, we introduce and study the absorbent and regular absorbent Г-semigroups. We approach this problem by examining quasi-ideals using Green＇s relations.
基金Project supported by the National Natural Science Foundation of China.
文摘Left (right) C-semigroups are the regular semigroups satisfying the following condition:eSSe (SeeS) for every e∈E (the set of idempotents of S). Refs. [1, 2] give the left(right) semi-spined product structure and the left (right) △-product structure of a left(right) C-semigroup, respectively. It is easy to see that the above condition defining a reg-ular semigroup S to be a left (right) C-semigroup may be replaced by the following condi-tion:
文摘The investigation of U-ample ω-semigroups is initiated. After obtaining some properties of such semigroups, a structure of U-ample ω-semigroups is established. It is proved that a semigroup is a U-ample ω-semigroup if and only if it can be expressed by WBR（T, 0）, namely, the weakly Bruck-Reilly extensions of a monoid T. This result not only extends and amplifies the structure theorem of bisimple inverse ω-semigroups given by N. R. Reilly, but also generalizes the structure theorem of ,-bisimple type A ω-semigroups given by U. Asibong-Ibe in 1985.
