The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are compute...The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are computed. In addition, the author proves that the spectra of Toeplitz operators with C^1-symbols are always connected, and discusses the algebraic prop-erties of Toeplitz operators.In particular, it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and Tψ^* = Tψ^- if and only if Tψ is a scalar operator.展开更多
Diagonal invariant ideals of Toeplitz algebras defined on discrete groups are introduced and studied. In terms of isometric representations of Toeplitz algebras associated with quasi-ordered groups, a character of a d...Diagonal invariant ideals of Toeplitz algebras defined on discrete groups are introduced and studied. In terms of isometric representations of Toeplitz algebras associated with quasi-ordered groups, a character of a discrete group to be amenable is clarified. It is proved that when G is Abelian, a closed two-sided non-trivial ideal of the Toeplitz algebra defined on a discrete Abelian ordered group is diagonal invariant if and only if it is invariant in the sense of Adji and Murphy, thus a new proof of their result is given.展开更多
The automorphism group of the C* -algebra generated by the Toeplitz operatos with symbols being continuous functions on the bicircle is characterized completely. The investigation is based on the analysis of the behav...The automorphism group of the C* -algebra generated by the Toeplitz operatos with symbols being continuous functions on the bicircle is characterized completely. The investigation is based on the analysis of the behaviour of an automorphism of the Toeplitz algebra on itsC* -ideal chains, and the state of the closed ideals in .展开更多
In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each mini...In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a monomial.Furthermore,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)N.We also give some interesting examples.展开更多
Let （G, G＋） be a quasi-partial ordered group such that G＋^0=G＋∩G＋^-1 is a non-trivial subgroup of G. Let [G] be the collection of left cosets and [G＋] be its positive. Denote by T^G＋ and T^[G＋] the associate...Let （G, G＋） be a quasi-partial ordered group such that G＋^0=G＋∩G＋^-1 is a non-trivial subgroup of G. Let [G] be the collection of left cosets and [G＋] be its positive. Denote by T^G＋ and T^[G＋] the associated Toeplitz algebras. We prove that T^G＋ is unitarily isomorphic to a C^＊-subalgebra of T^｜G＋｜⊙（G＋^＋） if there exists a deformation retraction from G onto G＋^0. Suppose further that G＋^0 is normal, then ,T^G＋ and ,T^｜G＋｜⊙GT^＊（G＋^0） are unitarily equivalent.展开更多
Let G be a discrete group, E1 and E2 be two subsets of G with E1 () E2, and e ∈ E2. Denote by TE1 and TE2 the associated Toeplitz algebras. In this paper, it is proved that the natural morphism γE2,E1 from TE1 to TE...Let G be a discrete group, E1 and E2 be two subsets of G with E1 () E2, and e ∈ E2. Denote by TE1 and TE2 the associated Toeplitz algebras. In this paper, it is proved that the natural morphism γE2,E1 from TE1 to TE2 exists as a C*-morphism if and only if E2 is finitely covariant-lifted by E1. Based on this necessary and sufficient condition, some applications are made.展开更多
The automorphism group of the Toeplitz algebra generated by the Toeplitz operators, whose symbols are continuous functions on the circle beside finitely fixed points, is characterized.
文摘The automorphism group of the Toeplitz C^*- algebra, J(C^1), generated by Toeplitz op-erators with C^1-symbols on Dirichlet space D is discussed; the K0, K1-groups and the first cohomology group of J(C^1) are computed. In addition, the author proves that the spectra of Toeplitz operators with C^1-symbols are always connected, and discusses the algebraic prop-erties of Toeplitz operators.In particular, it is proved that there is no nontrivial selfadjoint Toeplitz operator on D and Tψ^* = Tψ^- if and only if Tψ is a scalar operator.
基金The author thanks Nico Spronk for his help. This work was supported by theNational Natural Science Foundation of China (Grant No. 19901019) the Science and Technology Foundation of Shanghai Higher Education.
文摘Diagonal invariant ideals of Toeplitz algebras defined on discrete groups are introduced and studied. In terms of isometric representations of Toeplitz algebras associated with quasi-ordered groups, a character of a discrete group to be amenable is clarified. It is proved that when G is Abelian, a closed two-sided non-trivial ideal of the Toeplitz algebra defined on a discrete Abelian ordered group is diagonal invariant if and only if it is invariant in the sense of Adji and Murphy, thus a new proof of their result is given.
文摘The automorphism group of the C* -algebra generated by the Toeplitz operatos with symbols being continuous functions on the bicircle is characterized completely. The investigation is based on the analysis of the behaviour of an automorphism of the Toeplitz algebra on itsC* -ideal chains, and the state of the closed ideals in .
文摘In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a monomial.Furthermore,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)N.We also give some interesting examples.
基金the National Natural Foundation of China (10371051)Shanghai Natural Science Foundation (05ZR14094) and Shanghai Municipal Education Commission (05DZ04)
文摘Let （G, G＋） be a quasi-partial ordered group such that G＋^0=G＋∩G＋^-1 is a non-trivial subgroup of G. Let [G] be the collection of left cosets and [G＋] be its positive. Denote by T^G＋ and T^[G＋] the associated Toeplitz algebras. We prove that T^G＋ is unitarily isomorphic to a C^＊-subalgebra of T^｜G＋｜⊙（G＋^＋） if there exists a deformation retraction from G onto G＋^0. Suppose further that G＋^0 is normal, then ,T^G＋ and ,T^｜G＋｜⊙GT^＊（G＋^0） are unitarily equivalent.
基金Project supported by the National Natural Science Foundation of China (No.10371051).
文摘Let G be a discrete group, E1 and E2 be two subsets of G with E1 () E2, and e ∈ E2. Denote by TE1 and TE2 the associated Toeplitz algebras. In this paper, it is proved that the natural morphism γE2,E1 from TE1 to TE2 exists as a C*-morphism if and only if E2 is finitely covariant-lifted by E1. Based on this necessary and sufficient condition, some applications are made.
基金the National Natural Science Foundation of China ( Grant Nos. 19971061 and 19631070) Funds for Young Fellow of Sichuan University the Natural Science Foundation of Guangxi.
文摘The automorphism group of the Toeplitz algebra generated by the Toeplitz operators, whose symbols are continuous functions on the circle beside finitely fixed points, is characterized.
