The Rigidity of the Kernels of the Natural Morphisms between Toeplitz Algebras

Let (G, E) be a quasi-ordered group such that E∩E -1 is infinite, (G, G +) an ordered group with G +EG, and (G, G 1) the partially ordered group induced by (G, E).Let γ E, G + ∶T G + →T E and γ E, G 1 ∶T G 1 →T E be the corresponding natural morphisms between Toeplitz algebras. We prove that the kernel Ker γ E, G + is rigid,while Ker γ E, G 1 is equal to the compact-operator ideal on 2(G 1), and all Fredholm operators in the Toeplitz algebra T G 1 are of index zero.

Deformation Retraction of Groups and Toeplitz Algebras

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.

Twisted Semigroup Crossed Products and Twisted Toeplitz Algebras of Ordered Groups

Let г^＋ be the positive cone of a totally ordered abelian group г, and σa cocycle in г. We study the twisted crossed products by actions of г＋ as endomorphisms of C^＊-algebras, and use this to generalize the theorem of Ji.

THE MINIMAL CLOSED NON-TRIVIAL IDEALS OF TOEPLITZ ALGEBRAS ON DISCRETE GROUPS

Let G be a discrete group and (G, G+) an ordered group. Let (G, GF) be the minimal quasiordered group containing (G, G+). Let G+ (G) and (G) be the corresponding Toeplitz algebras, and γGF,G+ the natural C*-algebra morphism from G+ (G) to GF(G). This paper studies the connection between Ker GF,G+ and the minimal closed ideal ofTG+ (G). It is proved that if G is amenable and GF≠G+, then Ker γGF,G+ is exactly the minimal closed non-trivial ideal of G+ (G). As an application, in the last part of this paper, a character of K-groups of Toeplitz algebras on ordered groups is clarified.

Automorphisms of the Toeplitz algebra with piecewise continuous symbol

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.

TOEPLITZ ALGEBRAS ON DISCRETE GROUPS AND THEIR NATURAL MORPHISMS

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.

Diagonal invariant ideals of Toeplitz algebras on discrete groups

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.

The automorphism group of the Toeplitz algebra on H2(T2)

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 .

Automorphism group on the Toeplitz algebras

Let B be the unit ball of Cn, S2n-1 the unit sphere of Cn. The concept of the Toeplitzoperators on Hardy space H2(S2n-1) is as usual. Denote by C(S2n-1) the algebra of all con-tinuous functions on S2n-1, and (C(S2n-1)) the C*-algebra generated by the

TOEPLITZ OPERATORS ASSOCIATED WITH SEMIFINITE VON NEUMANN ALGEBRA

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.

Groupoid structure of Toeplitz algebra over L-shaped domain

The structure of the groupoid G associated with the Toeplitz C* -algebra C*(Ω) of the L-shaped domain is discussed. The detailed characterization of M∞ by the classification of the closed subgroup of the Euclidean space is presented.

群上的Toeplitz代数(英文)

研究了离散交换群上的Toeplitz算子和Toeplitz代数 .通过谱投影和Fourier变换 ,将离散交换群上的Toeplitz算子和Toeplitz代数的问题化成了其对偶群上的Hardy空间中的相应问题 ,并由此得到了Toeplitz算子的特征 (定理 10 ) ,约化Toeplitz代数与Toeplitz代数相等的充分必要性 (命题 5 )以及关于Toeplitz代数的短正合列(定理 6 )等一系列结果 .

解析Toeplitz算子的强不可约性(英文)

本文得到解析Toeplitz算子的强不可约性的一个充分条件,并且刻画了换位代数的k_0-群.

离散群上的Toeplitz算子代数的顺从性(英文)

设(G,G+)为一个拟格序群,H为G+的一个可传、定向子集．记GH=G+.H-1, 令TGH为相应的Toeplitz算子代数．利用G+的等距协变表示刻画了(G,GH)的顺从性。当 G=G+.G+-1时,证明了(G,GH)为顺从当且仅当G为顺从．

多重调和Bergman空间上的Toeplitz算子和Hankel算子

完全刻画多重调和Bergman空间上Toeplitz算子和Hankel算子的紧性.运用紧Toeplitz算子这个结果,建立了Toeplitz代数和小Hankel代数的短正合列,推广了单位圆盘上相应的结果.

具拟不变测度群胚流上的Toeplitz代数(英文)

设Ｇ为第二可数群胚，具有Ｈａａｒ系｛λｎ｝，Ｒ为实数群，左不变作用在Ｇ上．本文我们自然地（作为［３］中概念的推广）引进两类Ｔｏｅｐｌｉｔｚ代数（对应于一拟不变测度），即小和大Ｔｏｅｐｌｉｔｚ代数，并且得到了小Ｔｏｅｐｌｉｔｚ代数的同构定理及Ｘ群．

Fell丛上的拓扑分次Toeplitz交错代数(英文)

设B=(Bt)t∈Γ为离散群Γ上的一个Fell丛.任取Γ的一个非空子集E,定义了一个Toeplitz交错代数T E.证明了若给定的Fell丛B=(Bt)t∈Γ关于E是正则的,则相应的Toeplitz交错代数T E是拓扑分次的.

Toeplitz算子代数的忠实表示(英文)

设(G,G_+)为一个拟格序群,H为G_+的可传定向子集,令C_H=G_+·H^(-1),~H为相应的Toeplitz算子代数.作者刻划了~H的忠实表示。

具有有界径向符号的Toeplitz算子

研究由某些本质有界的径向函数为符号函数的Ｔｏｅｐｌｉｔｚ算子所生成的Ｃ

加权Bergman空间上的Toeplitz代数

本文讨论了加权Bergman空间上的Toeplitz代数J(C( D) ) ,得到正合列O→K→J(C( D) )→C( D) ) /C0 (D) )→ ,作为应用 ,刻划了Toeplitz代数算子的本质谱 .