The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(...The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.展开更多
In this paper,cohyponormal weighted composition operators on the Fock space over C^(N)are characterized completely.We also consider a class of weighted composition operators on the Fock space over C^(N)which are both ...In this paper,cohyponormal weighted composition operators on the Fock space over C^(N)are characterized completely.We also consider a class of weighted composition operators on the Fock space over C^(N)which are both posinormal and coposinormal.As an application,we obtain the characterization of hyponormal,cohyponormal,posinormal and coposinormal composition operators on the Fock space over C^(N).展开更多
We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applic...We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.展开更多
We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit p...We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ＂computable＂ estimates on the operator norm.展开更多
We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the op...We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H^1 to H^1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.展开更多
We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to ...This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.展开更多
This paper studies a class of weighted composition operators and their spectrum on the Fock space. As an application, bounded self-adjoint, a class of complex symmetric weighted composition operators on the Fock space...This paper studies a class of weighted composition operators and their spectrum on the Fock space. As an application, bounded self-adjoint, a class of complex symmetric weighted composition operators on the Fock space are characterized.展开更多
In this paper,we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients.The Hermitianness,Fredholmness and invertibility of such operators are characterized,and...In this paper,we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients.The Hermitianness,Fredholmness and invertibility of such operators are characterized,and the spectra of compact and invertible weighted composition operators are also described.展开更多
Based on a new characterization of bounded and compact weighted compositionoperators on the Fock space obtained by Le T （Le T. Normal and isometricweighted composition operators on the Fock space. Bull. London. Math....Based on a new characterization of bounded and compact weighted compositionoperators on the Fock space obtained by Le T （Le T. Normal and isometricweighted composition operators on the Fock space. Bull. London. Math. Soc., 2014,46： 847-856）, this paper shows that a bounded weighted composition operator onthe Fock space is a Fredholm operator if and only if it is an invertible operator, andif and only if it is a nonzero constant multiple of a unitary operator. The result isvery different from the corresponding results on the Hardy space and the Bergmanspace.展开更多
The article not only presents the boundedness and compactness of the weighted composition operator from α-Bloch spaces（or little α-Bloch spaces） to H^∞, but also gives some estimates for the norm of the weighted ...The article not only presents the boundedness and compactness of the weighted composition operator from α-Bloch spaces（or little α-Bloch spaces） to H^∞, but also gives some estimates for the norm of the weighted composition operator.展开更多
In this paper, we give a necessary and sufficient condition for weighted composition operators Cu,φ to be boundedness on Bloch type spaces B^α. The theorem generalizes some previous results.
Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss ...Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.展开更多
This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition o...This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.展开更多
In this paper, we study the boundedness and estimate the essential norm of the differences of weighted composition operators from mixed-norm spaces to weighted-type spaces on the unit ball of CN.
The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a comb...The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a combination of several derivative weighted composition operators which acts on classic Bergman space,the lower bound of its essential norm is estimated in terms of the boundary data of the symbols of d-composition operators.Some similar results about composition operators on the Dirichlet space are also presented.A necessary condition is given to determine the compactness of the combination of several derivative weighted composition operators on Bergman spaces.展开更多
This paper characterizes bounded, Fredholm weighted composition operators on Hardy space. As an application, the Fredholm index of such operators is obtained.
In this paper,we study bounded(linear and anti-linear)weighted composition operators on the symmetric Fock space over a separable Hilbert space.The unitary and self-adjoint weighted composition operators are character...In this paper,we study bounded(linear and anti-linear)weighted composition operators on the symmetric Fock space over a separable Hilbert space.The unitary and self-adjoint weighted composition operators are characterized completely.A class of normal weighted composition operators is considered.展开更多
In this paper, we characterize weighted composition operators that preserve frames on the weighted Hardy spaces in the unit disk. In particular, we obtain the symbol properties of the bounded invertible weighted compo...In this paper, we characterize weighted composition operators that preserve frames on the weighted Hardy spaces in the unit disk. In particular, we obtain the symbol properties of the bounded invertible weighted composition operators. Moreover, we establish the equivalence between bounded invertible operators and frame-preserving operators. Furthermore, we show that weighted composition operator preserves frames if and only if it preserves the Riesz bases property. Additionally,we investigate the weighted composition operators that preserve tight or normalized tight frames on the Dirichlet space.展开更多
基金Supported by Sichuan Science and Technology Program (No.2022ZYD0010)。
文摘The aim of the present paper is to study 2-complex symmetric bounded weighted composition operators on the Fock space of C^(N) with the conjugations J and J_(t,A,b) defined by ■ respectively,where k(z_(1),...,z_N)=(■,...,■),t∈C,b∈C^(N) and A is a linear operator on C^(N).An example of 2-complex symmetric bounded weighted composition operator with the conjugation J_(t,A,b) is given.
基金Supported by the National Natural Science Foundation of China(Grant No.12271134)Shanxi Scholarship Council of China(Grant No.2020-089)Program of Graduate Bilingual Curriculum Construction in Shanxi Normal University(Grant No.YJSSY201903).
文摘In this paper,cohyponormal weighted composition operators on the Fock space over C^(N)are characterized completely.We also consider a class of weighted composition operators on the Fock space over C^(N)which are both posinormal and coposinormal.As an application,we obtain the characterization of hyponormal,cohyponormal,posinormal and coposinormal composition operators on the Fock space over C^(N).
文摘We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.
文摘We study the bounded and the compact weighted composition operators from the Bloch space into the weighted Banach spaces of holomorphic functions on bounded homogeneous domains, with particular attention to the unit polydisk. For bounded homogeneous domains, we characterize the bounded weighted composition operators and determine the operator norm. In addition, we provide sufficient conditions for compactness. For the unit polydisk, we completely characterize the compact weighted composition operators, as well as provide ＂computable＂ estimates on the operator norm.
基金Supported in part by 973 plan and NSF of Zhejiang Province of China(Gl999075105)
文摘We consider the weighted composition operators between Hardy spaces on the unit ball, and obtain some sufficient and necessary conditions of bounded or compact weighted composition operators. We also prove that the operator from H^1 to H^1 is compact if and only if it is weakly compact. Meanwhile, we get the analogue on the Bergman spaces.
基金This work was supported by NSF of China(11171203,11201280)New Teacher’s Fund for Doctor Stations,Ministry of Education(20114402120003)NSF of Guangdong Province(10151503101000025,S2011010004511,S2011040004131)
文摘We characterize the boundedness and compactness of weighted composition operators on weighted Dirichlet spaces in terms of Nevanlinna counting functions and Caxleson measure.
基金Supported by the National Natural Science Foundation of China (10771064)the Natural Science Foundation of Zhejiang province (Y6090036+1 种基金Y7080197,Y606197)the Foundation of Department of Education of Zhejiang Province (20070482)
文摘This paper deals with the boundedness and compactness of the weighted composition operators from the F（p, q, s） spaces, including Hardy space, Bergman space, Qp space, BMOA space, Besov space and α-Bloch space, to Bers-type spaces Hv^∞（ or little Bers-type spaces Hv,o∞ ）, where v is normal.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1120127411471189)
文摘This paper studies a class of weighted composition operators and their spectrum on the Fock space. As an application, bounded self-adjoint, a class of complex symmetric weighted composition operators on the Fock space are characterized.
基金partially supported by NSFC(11771340,11701434,11431011,11471251,11771441)
文摘In this paper,we study weighted composition operators on the Hilbert space of Dirichlet series with square summable coefficients.The Hermitianness,Fredholmness and invertibility of such operators are characterized,and the spectra of compact and invertible weighted composition operators are also described.
文摘Based on a new characterization of bounded and compact weighted compositionoperators on the Fock space obtained by Le T （Le T. Normal and isometricweighted composition operators on the Fock space. Bull. London. Math. Soc., 2014,46： 847-856）, this paper shows that a bounded weighted composition operator onthe Fock space is a Fredholm operator if and only if it is an invertible operator, andif and only if it is a nonzero constant multiple of a unitary operator. The result isvery different from the corresponding results on the Hardy space and the Bergmanspace.
基金the National Natural Science Foundation of China(10471039)the Natural Science Foundation of Zhejiang Province(Y606197)the Natural Science Foundation of Huzhou City(2005YZ02)
文摘The article not only presents the boundedness and compactness of the weighted composition operator from α-Bloch spaces（or little α-Bloch spaces） to H^∞, but also gives some estimates for the norm of the weighted composition operator.
基金the Scientific Research Program of the Higher Education Institution of Xinjiang(XJEDU2005E06)
文摘In this paper, we give a necessary and sufficient condition for weighted composition operators Cu,φ to be boundedness on Bloch type spaces B^α. The theorem generalizes some previous results.
基金The NSF(11501136,11271092)of Chinathe Key Discipline Construction Project of Subject Groups Focus on Mathematics+1 种基金Information Science in the Construction Project(4601-2015)of the High-level University of Guangdong Provincethe Project(HL02-1517)for the New Talent of Guangzhou University
文摘Abstract： We characterize the boundedness and compactness of weighted compo-sition operators among some Fock-Sobolev spaces. We also estimate the norm and essential norm of these operators. Furthermore, we discuss the duality spaces of Fock-Sobolev spaces Fs^p,mwhen 0 〈 p 〈∞.
基金Supported by the NNSF of China(10471039)the Natural Science Foundation of Zhejiang Province(M103 104)the Natural Science Foundation of Huzhou City(2005YZ02).
文摘This paper characterizes the boundedness and compactness of weighted composition operators between Bers-type space （or little Bers-type space） and Bergman space. Some estimates for the norm of weighted composition operators between those spaces are obtained.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 1097115310671141)
文摘In this paper, we study the boundedness and estimate the essential norm of the differences of weighted composition operators from mixed-norm spaces to weighted-type spaces on the unit ball of CN.
基金Supported by National Natural Science Foundation of China (No. 10971153 and No. 10671141)
文摘The relation between composition operators on the Dirichlet spaces in the open unit disk and derivative weighted composition operators on the Bergman spaces in the open unit disk is investigated firstly,and for a combination of several derivative weighted composition operators which acts on classic Bergman space,the lower bound of its essential norm is estimated in terms of the boundary data of the symbols of d-composition operators.Some similar results about composition operators on the Dirichlet space are also presented.A necessary condition is given to determine the compactness of the combination of several derivative weighted composition operators on Bergman spaces.
基金Supported by the National Natural Science Foundation of China(Grant No.11201274)Young Science Foundation of Shanxi Province(Grant No.2010021002-2)
文摘This paper characterizes bounded, Fredholm weighted composition operators on Hardy space. As an application, the Fredholm index of such operators is obtained.
基金Supported by the National Natural Science Foundation of China(Grant No.11771401)Shanxi Scholarship Council of China(Grant No.2020-089)Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province(Grant No.20200019).
文摘In this paper,we study bounded(linear and anti-linear)weighted composition operators on the symmetric Fock space over a separable Hilbert space.The unitary and self-adjoint weighted composition operators are characterized completely.A class of normal weighted composition operators is considered.
基金supported by Nation Natural Science Foundation of China(Grant Nos.11671214,11971348,12071230)MOE(Ministry of Education in China)Youth Foundation Project of Humanities and Social Sciences(Grant No.19YJCZH111)。
文摘In this paper, we characterize weighted composition operators that preserve frames on the weighted Hardy spaces in the unit disk. In particular, we obtain the symbol properties of the bounded invertible weighted composition operators. Moreover, we establish the equivalence between bounded invertible operators and frame-preserving operators. Furthermore, we show that weighted composition operator preserves frames if and only if it preserves the Riesz bases property. Additionally,we investigate the weighted composition operators that preserve tight or normalized tight frames on the Dirichlet space.
