As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelope...As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H .展开更多
In this note,we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivi...In this note,we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivity,automorphism and finite rank operators.展开更多
Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U⊥, a complete description of the extreme points of the unit ball U1 is given.
Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated...Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated with M, we consider Toeplitz operators and the Hilbert transform associated with 8i. We prove that the commutant of left analytic Toeplitz algebra on noncommutative Hardy space H2（A4） is just the right analytic Toeplitz algebra. Furthermore, the Hilbert transform on noncommutative LP（Yt4） is shown to be bounded for 1 （ p （ ce. As an application, we consider a noncomnmtative analog of the space BMO and identify the dual space of noncommutative Hl（M） as a concrete space of operators.展开更多
In this paper, the Ext groups of Hardy modules over the polydisk algebra A(Dn) are cal-culated. Of particular importance is that the calculating of Ext-groups is closely related toharmonic analysis of polydisks. Final...In this paper, the Ext groups of Hardy modules over the polydisk algebra A(Dn) are cal-culated. Of particular importance is that the calculating of Ext-groups is closely related toharmonic analysis of polydisks. Finally, the authors point out that Ext-groups reveal rigidityof Hardy submodules over A(Dn) for n > 1.展开更多
The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coeff...The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X, where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.展开更多
Let B(H) be the algebra of all bounded linear operators on a complex separable infinite dimensional Hilbert space H.Denote by π the quotient map of B(H) onto the Calkin algebra A(H).In 1984,Apostol et al.raised the f...Let B(H) be the algebra of all bounded linear operators on a complex separable infinite dimensional Hilbert space H.Denote by π the quotient map of B(H) onto the Calkin algebra A(H).In 1984,Apostol et al.raised the following conjecture:If an operator T on H is not similar to a compact perturbation of a Jordan operator,then the similarity orbit of π(T) in A(H) coincides with the π-image of the similarity orbit of T.In this paper,we investigate the structure of similarity orbits in the Calkin algebra and give a negative answer to the above conjecture.展开更多
Based on the notion of free orbit-dimension of Hadwin-Shen (2007) we introduce a new invariant for finite von Neumann algebras with arbitrarily large generating sets and acting on Hilbert spaces of arbitrary dimension...Based on the notion of free orbit-dimension of Hadwin-Shen (2007) we introduce a new invariant for finite von Neumann algebras with arbitrarily large generating sets and acting on Hilbert spaces of arbitrary dimension. We show that this invariant is independent of the generating set, and we extend results in Hadwin-Shen (2007) to this larger class of algebras.展开更多
Let H be a Hilbert space and A ■ B(H) be a C~*-subalgebra. This paper is devoted to studying the set gP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curv...Let H be a Hilbert space and A ■ B(H) be a C~*-subalgebra. This paper is devoted to studying the set gP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curves. We prove that the space gP is a C~∞ Banach submanifold of A, and a homogeneous reductive space under the action of Banach Lie group U_A of A. Moreover, we compute the geodesics of gP in a standard fashion, and prove that any generalized projection in a prescribed neighbourhood of p∈gP can be joined with p by a unique geodesic curve in gP.展开更多
This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,i...This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,it is proved that if N, M are non-trivial then RN RM=R if and only if N, M are continuous.展开更多
Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S^(*n)T S^n}is convergent...Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S^(*n)T S^n}is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H.In this paper,we study the asymptotic T_u-Toeplitzness of weighted composition operators on the Hardy space H^2,where u is a nonconstant inner function.展开更多
文摘As in homology, the notion of injectivity is introduced in the category whose objects are Hilbert C * module over a C * algebra and whose morphism are bounded module operators. The definition of injective envelopes of an extension of a Hilbert C * modules over a C * algebra is introduced, and is characterized in terms of the injectivity and essence. It is shown that every Hilbert C * module has a unique (up to H isometrics) injective envelope if it exists. It is also shown that an extension of a Hilbert C * module is an injective envelope if and only if it is an injective and essential extension. Moreover, every Hilbert C * module over a W * algebra has a unique (up to H isometrics) injective envelope and the injective envelope of a Hilbert C * module H is maximal essential extension of H .
文摘In this note,we discuss some properties of reflexive algebras on a Hilbert space with invariant subspace lattices as realizations of the pentagon and the double triangle and give some results concerning hyperreflexivity,automorphism and finite rank operators.
文摘Suppose that U is a norm closed nest algebra module. Using the characterization of rank one operators in U⊥, a complete description of the extreme points of the unit ball U1 is given.
基金supported by National Natural Science Foundation of China(Grant No.11371233)the Fundamental Research Funds for the Central Universities(Grant No.GK201301007)
文摘Let M be a a-finite yon Neumann algebra and let 9i C M be a maximal subdiagonal algebra with respect to a faithful normal conditional expectation Ф. Based on the Haagerup＇s noncommutative Lp space LP（M） associated with M, we consider Toeplitz operators and the Hilbert transform associated with 8i. We prove that the commutant of left analytic Toeplitz algebra on noncommutative Hardy space H2（A4） is just the right analytic Toeplitz algebra. Furthermore, the Hilbert transform on noncommutative LP（Yt4） is shown to be bounded for 1 （ p （ ce. As an application, we consider a noncomnmtative analog of the space BMO and identify the dual space of noncommutative Hl（M） as a concrete space of operators.
文摘In this paper, the Ext groups of Hardy modules over the polydisk algebra A(Dn) are cal-culated. Of particular importance is that the calculating of Ext-groups is closely related toharmonic analysis of polydisks. Finally, the authors point out that Ext-groups reveal rigidityof Hardy submodules over A(Dn) for n > 1.
基金Project supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200416)the Program for New Century Excellent Talents in University of China (No. 06-0420)+2 种基金the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars (No.2008-890)the Dawn Light Project of Shanghai Municipal Education Commission (No. 07SG38)the Shanghai Pujiang Program (No. 08PJ14006).
文摘The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X, where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.
基金supported by National Natural Science Foundation of China(Grant Nos.10971079,11026038)the Basic Research Foundation of Jilin University(Grant No.201001001)the Young Fund of Department of Mathematics at Jilin University
文摘Let B(H) be the algebra of all bounded linear operators on a complex separable infinite dimensional Hilbert space H.Denote by π the quotient map of B(H) onto the Calkin algebra A(H).In 1984,Apostol et al.raised the following conjecture:If an operator T on H is not similar to a compact perturbation of a Jordan operator,then the similarity orbit of π(T) in A(H) coincides with the π-image of the similarity orbit of T.In this paper,we investigate the structure of similarity orbits in the Calkin algebra and give a negative answer to the above conjecture.
文摘Based on the notion of free orbit-dimension of Hadwin-Shen (2007) we introduce a new invariant for finite von Neumann algebras with arbitrarily large generating sets and acting on Hilbert spaces of arbitrary dimension. We show that this invariant is independent of the generating set, and we extend results in Hadwin-Shen (2007) to this larger class of algebras.
基金supported by National Natural Science Foundation of China(Grant No.11371233)
文摘Let H be a Hilbert space and A ■ B(H) be a C~*-subalgebra. This paper is devoted to studying the set gP of generalized projections in A from a differential geometric point of view, and mainly focuses on geodesic curves. We prove that the space gP is a C~∞ Banach submanifold of A, and a homogeneous reductive space under the action of Banach Lie group U_A of A. Moreover, we compute the geodesics of gP in a standard fashion, and prove that any generalized projection in a prescribed neighbourhood of p∈gP can be joined with p by a unique geodesic curve in gP.
文摘This paper studies the tensor product RN RM of Jacobson radicals in nest algebras, and obtains that RN RM = {T∈B(H1 H2) : T(N M)(?)N_ M_, N∈N,M∈M}; and based on the characterization of rank-one operators in RN RM,it is proved that if N, M are non-trivial then RN RM=R if and only if N, M are continuous.
基金supported by Hankuk University of Foreign Studies Research Fund
文摘Given a unilateral forward shift S acting on a complex,separable,infinite dimensional Hilbert space H,an asymptotically S-Toeplitz operator is a bounded linear operator T on H satisfying that{S^(*n)T S^n}is convergent with respect to one of the topologies commonly used in the algebra of bounded linear operators on H.In this paper,we study the asymptotic T_u-Toeplitzness of weighted composition operators on the Hardy space H^2,where u is a nonconstant inner function.
