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Hyponormal Block Toeplitz Operators on the Weighted Bergman Space with Circulant Symbols 认领 引用
1
作者 FU Guangyang ZHOU Jiang 《数学进展》 CSCD 北大核心 2026年第1期183-191,共9页
In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G*(z)+F(z),where F(z)=∑Ni=1 Aiziand... In this paper,we present a necessary and sufficient condition for hyponormal block Toeplitz operators T on the vector-valued weighted Bergman space with symbolsΦ(z)=G*(z)+F(z),where F(z)=∑Ni=1 Aiziand G(z)=∑Ni=1 A−izi,Aiae culants. 展开更多
关键词 block Toeplitz operator hyponormal weighted Bergman space circulant commutator
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The Hyponormal Block Dual Toeplitz Operators 认领 引用
2
作者 Yingliang FU Puyu CUI +1 位作者 Chao ZU Yufeng LU 《Journal of Mathematical Research with Applications》 CSCD 2025年第3期377-394,共18页
We consider the hyponormality of the block dual Toeplitz operator SΦacting on the orthogonal complement of the vector valued weighted Bergman space (Aα2(D,Cn))⊥.We provide a necessary and sufficient ... We consider the hyponormality of the block dual Toeplitz operator SΦacting on the orthogonal complement of the vector valued weighted Bergman space (Aα2(D,Cn))⊥.We provide a necessary and sufficient condition for the hyponormality of SΦwith matrix valued bounded harmonic symbol.In this process,we introduce a function gw,s∈(Aα2(D))⊥,which is similar to the reproducing kernel of the weighted Bergman space Aα2(D).We also give some additional applications of the function gw,s∈(Aα2(D))⊥. 展开更多
关键词 vector-valued weighted Bergman space Hyponormality block dual Toeplitz operators
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APPLICATION OF TWO OPERATORS TRANSFORM FROM CLASS A OPERATOR TO THE CLASS OF HYPONORMAL OPERATOR 认领 引用 被引量：1
3
作者 杨长森 丁艳风 《Acta Mathematica Scientia》 SCIE CSCD 2011年第1期93-101,共9页
In this article, we give an operator transform T （＊） from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that... In this article, we give an operator transform T （＊） from class A operator to the class of hyponormal operators. It is different from the operator transform T defined by M. Ch and T. Yamazaki. Then, we show that σ（T ） = σ（ T （＊）） and σa（T ）／{0} = σa（ T （＊））／{0}, in case T belongs to class A. Next, we obtain some relations between T and T （9）. 展开更多
关键词 Class A operator hyponormal p-hyponormal polar decomposition numerical radius
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HYPONORMALITY OF BLOCK TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES 认领 引用 被引量：2
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作者 Jongrak LEE 《Acta Mathematica Scientia》 SCIE CSCD 2017年第6期1695-1704,共10页
In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in... In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in the class of functions Ф=F ＋ G＊ withmatrix-valued polynomial functions F and G with degree 2. 展开更多
关键词 block Toeplitz operators hyponormal weighted Bergman space
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Cohyponormal Weighted Composition Operators on the Fock Space over CN 认领 引用
5
作者 Lixia FENG Liankuo ZHAO 《Journal of Mathematical Research with Applications》 CSCD 2024年第2期239-247,共9页
In this paper,cohyponormal weighted composition operators on the Fock space over CNare characterized completely.We also consider a class of weighted composition operators on the Fock space over CNwhich are both ... In this paper,cohyponormal weighted composition operators on the Fock space over CNare characterized completely.We also consider a class of weighted composition operators on the Fock space over CNwhich 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 CN. 展开更多
关键词 Fock space weighted composition operator hyponormal cohyponormal posinormal coposinormal
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Spectral Characterization of Hyponormal Weighted Shifts 认领 引用
6
作者 王公宝 《Chinese Quarterly Journal of Mathematics》 2002年第2期65-70,共6页
The complete characterizations of the spectra and their various parts of hyponormal unilateral and bilateral weighted shifts are presented respectively in this paper. The results obtained here generalize the correspon... The complete characterizations of the spectra and their various parts of hyponormal unilateral and bilateral weighted shifts are presented respectively in this paper. The results obtained here generalize the corresponding work of the references. 展开更多
关键词 Hilbert space hyponormal operators weighted shifts spectrum
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ON REFLEXIVITY OF HYPONORMAL AND WEIGHTED SHIFT OPERATORS 认领 引用 被引量：1
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作者 M.Faghih Ahmadi K.Hedayatian 《Acta Mathematica Scientia》 SCIE 2010年第4期1100-1104,共5页
By an elementary proof, we use a result of Conway and Dudziak to show that if A is a hyponormal operator with spectral radius r（A） such that its spectrum is the closed disc {z：｜z｜ ≤ r（A）} then A is reflexive. ... By an elementary proof, we use a result of Conway and Dudziak to show that if A is a hyponormal operator with spectral radius r（A） such that its spectrum is the closed disc {z：｜z｜ ≤ r（A）} then A is reflexive. Using this result, we give a simple proof of a result of Bercovici, Foias, and Pearcy on reflexivity of shift operators. Also, it is shown that every power of an invertible bilateral weighted shift is reflexive. 展开更多
关键词 Reflexivity of hyponormal operators bilateral weighted shift Laurent series
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Weakly k-hyponormal and polynomially hyponormal commuting operator pairs 认领 引用
8
作者 DUAN Yong Jiang QI Ting Ting 《Science China Mathematics》 SCIE CSCD 2015年第2期405-422,共18页
We introduce the notion of weak k-hyponormality and polynomial hyponormality for commuting operator pairs on a Hilbert space and investigate their relationship with k-hyponormality and subnormality.We provide examples... We introduce the notion of weak k-hyponormality and polynomial hyponormality for commuting operator pairs on a Hilbert space and investigate their relationship with k-hyponormality and subnormality.We provide examples of 2-variable weighted shifts which are weakly 1-hyponormal but not hyponormal.By relating the weak k-hyponormality and k-hyponormality of a commuting operator pair to positivity of restriction of some linear functionals to corresponding cones of functions,we prove that there is an operator pair that is polynomially hyponormal but not 2-hyponormal,generalizing Curto and Putinar’s result(1991,1993)to the two-variable case. 展开更多
关键词 weakly k-hyponormal k-hyponormal polynomially hyponormal subnormal commuting operator pair
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Hyponormal Toeplitz Operators on the Polydisk 认领 引用
9
作者 Yu Feng LU Yan Yue SHI 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第2期333-348,共16页
By bounded vector-valued functions and block matrix representations of Hankel operators, we completely characterize the hyponormality of Toeplitz operators on the Hardy space of the polydisk.
关键词 Hyponormality Toeplitz operator Hankel operator polydisk block matrix representation
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A GUESS ON HYPONORMAL OPERATOR TUPLES 认领 引用
10
作者 李绍宽 《Chinese Science Bulletin》 1992年第6期445-447,共3页
For a hyponormal operator T if there is a polynomial p(·) such that σ(p(T))= {0}, then p(T) =0. In general, it is proved in this way: from σ(p(T)) =0, we know that σ(T) consists of finite points, and therefore... For a hyponormal operator T if there is a polynomial p(·) such that σ(p(T))= {0}, then p(T) =0. In general, it is proved in this way: from σ(p(T)) =0, we know that σ(T) consists of finite points, and therefore T must be normal and so is p(T), hence p(T) =0. 展开更多
关键词 hyponormal operator normal operator spectrum
Hyponormal Dual Toeplitz Operators on the Orthogonal Complement of the Harmonic Bergman Space 认领 引用 被引量：3
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作者 Chong Chao WANG Xian Feng ZHAO 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第5期846-862,共17页
In this paper,we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space.First we show that the dual Toeplitz operator with the bounded symbol is hyponormal... In this paper,we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space.First we show that the dual Toeplitz operator with the bounded symbol is hyponormal if and only if it is normal.Then we obtain a necessary and sufficient condition for the dual Toeplitz operator Sφ with the symbol φ(z)=azn1zm1+bzn2zm2(n1,n2,m1,m2∈N and a,b∈C)to be hyponormal.Finally,we show that the rank of the commutator of two dual Toeplitz operators must be an even number if the commutator has a finite rank. 展开更多
关键词 Dual Toeplitz operator harmonic Bergman space normal hyponormal
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Hyponormality of Toeplitz Operators on the Dirichlet Space 认领 引用
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作者 Qiao Fei LU Tao YU 《Journal of Mathematical Research and Exposition》 CSCD 2011年第6期1057-1063,共7页
In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Diric... In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant. 展开更多
关键词 Toeplitz operator hyponormality Dirichlet space harmonic Dirichlet space
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On Hyponormal Weighted Unilateral Shift of Multiplicity K(0 认领 引用
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作者 郑德超 《Acta Mathematica Sinica,English Series》 SCIE 1987年第1期77-81,共5页
It is shown in[6]and[7]that a necessary and sufficient condition for a hyponormal weightedunilateral shift to be unitarily equivalent to a Toeplitz operator is that its weights satisfy(1-|an|2)=(1-|a0|2)(1-|an-1|2)n≥... It is shown in[6]and[7]that a necessary and sufficient condition for a hyponormal weightedunilateral shift to be unitarily equivalent to a Toeplitz operator is that its weights satisfy(1-|an|2)=(1-|a0|2)(1-|an-1|2)n≥1,where ansatisfiesan=1.In[8],the author obtainedsimilar result for the hyponormal weighted unilateral shift of multiplicity 2.The aim of this 展开更多
关键词 On Hyponormal Weighted Unilateral Shift of Multiplicity K
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TOEPLITZ OPERATORS ASSOCIATED WITH SEMIFINITE VON NEUMANN ALGEBRA 认领 引用 被引量：2
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作者 闫成 吐尔德别克 《Acta Mathematica Scientia》 SCIE CSCD 2015年第1期182-188,共7页
Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm... Let H^2（M） be a noncommutative Hardy space associated with semifinite von Neumann algebra M, we get the connection between numerical spectrum and the spectrum of Toeplitz operator Tt acting on H^2（M）, and the norm of Toeplitz operator Tt is equivalent to ｜｜t｜｜ when t is hyponormal operator in M. 展开更多
关键词 numerical spectrum hyponormal toeplitz operator semifinite yon Neumann algebra noncommutative Hardy space
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全Fock空间中生成子的谱研究 认领 引用
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作者 耿德文 闫成 《新疆大学学报（自然科学版中英文）》 CAS 2023年第2期169-174,共6页
借助hyponormal算子的谱的性质,对全Fock空间中生成子的谱的相关性质进行研究,得出生成子的近似点谱包含在复平面中以原点为心半径1的方体内.
关键词 全Fock空间 生成子 湮灭子 hyponormal算子 谱
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ON A PROBLEM OF N.SALINAS 认领 引用
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作者 史平 《Journal of Southeast University(English Edition)》 CAS 1989年第2期25-31,共7页
This paper presents a discussion on a problem suggested by N.Salinas（J.Operator Theory,Vol.10,1983）,i.e.,if T=（T1,T2,…,Tn）is a commuting n-tuple ofhyponormal operators on a complex Hilbert space,do we have（1）（... This paper presents a discussion on a problem suggested by N.Salinas（J.Operator Theory,Vol.10,1983）,i.e.,if T=（T1,T2,…,Tn）is a commuting n-tuple ofhyponormal operators on a complex Hilbert space,do we have（1）（2）δ（T-μ）=dist（μ,σl（T））,μ∈Cn?It is proved that the problems（1）and（2）are both true for some commuting n-tuples ofsemihyponormal operators.In general case,problem（1）has a negative answer.As an ap-plication,we point out that there exists a commuting n-tuple of hyponormal operatorsT（n≥2）,such that|λ|【,where σT（T）denotes J.L.Taylor’sjoint spectra of T,even if the condition of Taylor’s joint spectra of T is given. 展开更多
关键词 commuting n-tuples of(semi)hyponormal operators Taylor’s joint spectra joint spectra
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Near Subnormality of Weighted Shifts and the Answer to the Hilbert Space Problem 160 认领 引用 被引量：1
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作者 王公宝 马吉溥 《Northeastern Mathematical Journal》 2001年第1期45-48,共4页
In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented a... In this paper, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal. As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper. 展开更多
关键词 weighted shift near subnormal operator subnormal operator hyponormal operator M P generalized inverse
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Reflexivity of Operator Weighted Shifts 认领 引用
18
作者 Li Juexian Zhao Tianxia 《Northeastern Mathematical Journal》 1995年第4期483-488,共6页
In this paper,we describe the eigenvalues of an operator weighted Shift and give some sufficient conditions for an operator weighted shift to be reflexive.We also show that every hyponomal operator weighted shift is r... In this paper,we describe the eigenvalues of an operator weighted Shift and give some sufficient conditions for an operator weighted shift to be reflexive.We also show that every hyponomal operator weighted shift is reflexive. 展开更多
关键词 Reflexive Operator Hyponormal Operator Operator Weighted Shift
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Algebraic Properties of Toeplitz Operators on Discrete Commutative Groups 认领 引用
19
作者 GUO Xun Xiang 《Journal of Mathematical Research and Exposition》 北大核心 2008年第2期396-402,共7页
In this paper,a generalized Toeplitz operator is defined and some of results about the classical Toeplitz operator are generalized.In particular,we obtain the necessary and sufficient condition for the product of two ... In this paper,a generalized Toeplitz operator is defined and some of results about the classical Toeplitz operator are generalized.In particular,we obtain the necessary and sufficient condition for the product of two such Toeplitz operators to still be Toeplitz operator and the necessary and sufficient condition for such Toeplitz operator to be normal operator.Finally,a necessary condition for two such Toeplitz operators to be commutative is established. 展开更多
关键词 discrete commutative group almost stable subset Toeplitz operator hyponormal operator Hankle operator analytic Toeplitz operator
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Completely Non-Normal Toeplitz Operators 认领 引用
20
作者 Yah Yue SHI Yu Feng LU 《Journal of Mathematical Research and Exposition》 CSCD 2011年第4期727-734,共8页
In this paper, we show that the hyponormal Toeplitz operator Tφ with trigonometric polynomial symbol φ is either normal or completely non-normal. Moreover, if Tφ is non-normal, then Tφ has a dense set of cyclic ve... In this paper, we show that the hyponormal Toeplitz operator Tφ with trigonometric polynomial symbol φ is either normal or completely non-normal. Moreover, if Tφ is non-normal, then Tφ has a dense set of cyclic vectors. Some general conditions are also considered. 展开更多
关键词 Toeplitz operator completely nononormal hyponormal cyclic.
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