块对偶Toeplitz算子的乘积

本文刻画了向量值Bergman空间上块对偶Toeplitz算子有界性和紧性,给出了块对偶Toeplitz算子的乘积是块对偶Toeplitz算子的充要条件.     

单位圆盘加权Bergman空间上Toeplitz算子的本性范数

对于D上的Carleson测度μ而言,本文研究在加权Bergman空间Aα~2（D）上具有符号μ的Toeplitz算子Tμ的一些特殊的性质.近几年,在加权Bergman空间Aα~2（D）上的Toeplitz算子的有界性和紧性已经被广泛研究.为了了解Toeplitz算子Tμ的一些其他性质,本文需要估算出单位圆盘的加权Bergman空间上Toeplitz算子的本性范数的界限.     

调和Dirichlet空间上Toeplitz算子与小Hankel算子的交换性

本文研究了调和Dirichlet空间上调和符号的Toeplitz算子与小Hankel算子交换性的问题.利用算子矩阵表示的方法,获得了调和Dirichlet空间上调和符号的Toeplitz算子与小Hankel算子交换的充要条件,将Dirichlet空间上的相应结果推广到了调和Dirichlet空间上.     

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.     

Dirichlet型空间上Toeplitz算子的本性范数

本文研究单位圆盘上Dirichlet型空间非紧Toeplitz算子的本性范数, 它事实上等于到紧Toeplitz算子集的距离. 并且这个距离可由无限多个紧Toeplitz算子来刻画, 这个结果与加权Bergman空间情形的类似.     

Dirichlet空间上的Bergman型Toeplitz算子

本文给出了Dirichlet空间上以有界调和函数为符号的Bergman型Toeplitz算子是紧算子的充要条件.同时刻画了此类Bergman型Toeplitz算子在Dirichlet空间上的交换性.     

Diricher空间上Toeplitz算子的若干问题

讨论了Dirichlit空间上Toeplitz算子的紧性,特别地得到了Schatlen类Toeplitz算子的特征,此外,还证明了关于Toeplitz算子的一个非稠密性定理,并证明一个非零的函数可以诱导一个零算子,这与Hardy空间及Bergman空间情形是一重大差别。     

Dirichet空间上Toeplitz算子的若干问题

讨论了Dirichlet空间上Toeplitz算子的紧性,特别地得到了Schatlen类Toeplitz算子的特征.此外,还证明了关于Toeplitz算子的一个非稠密性定理,并证明一个非零的函数可以诱导一个零算子,这与Hardy空间及Bergman空间情形是一重大差别.     

Dirichlet空间上的Toeplitz算子

本文研究了Dirichlet空间上的Toeplitz算子,部分的回答了文[1]中的问题,给出了关于Dirichlet空间上Toeplitz算子的一个稠密性定理。     

多圆盘上Hardy空间上的Berezin变换和Toeplitz算子的交换性

,该文讨论多圆盘上Hardy空间上的Toeplitz算子,使用Berezin变换和调和扩张给出两个Toeplitz算子交换的一个充要条件.     

Hyponormal Toeplitz operators on the polydisk

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.     

A gap between hyponormality and subnormality for block Toeplitz operators

This paper concerns a gap between hyponormality and subnormality for block Toeplitz operators. We show that there is no gap between 2-hyponormality and subnormality for a certain class of trigonometric block Toeplitz operators (e.g., its co-analytic outer coefficient is invertible). In addition we consider the extremal cases for the hyponormality of trigonometric block Toeplitz operators: in this case, hyponormality and normality coincide.     

Hyponormal Dual Toeplitz Operators on the Orthogonal Complement of the Harmonic Bergman Space

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 ■ with the symbol ■ 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 fin...     

Joint Hyponormality of Toeplitz Pairs with Rational Symbols

In this note we consider joint hyponormality of pairs of Toeplitz operators acting on the Hardy space ${H^2(\mathbb T)}$ of the unit circle ${\mathbb T}$ . We give answers on some questions which arise from joint hyponormality of Toeplitz pairs with rational symbols.     

On hyponormal toeplitz operators with polynomial and symmetric-type symbols

This paper treats the hyponormality of Toeplitz operators that have polynomial symbols with symmetric-type sets of coefficients.     

Hyponormal Toeplitz Operators with Matrix-Valued Circulant Symbols

In this paper we are concerned with the hyponormality of Toeplitz operators with matrix-valued circulant symbols. We establish a necessary and sufficient condition for Toeplitz operators with matrix-valued partially circulant symbols to be hyponormal and also provide a rank formula for the self-commutator.     

Hyponormal Toeplitz operators and zeros of polynomials

The problem of hyponormality for Toeplitz operators with (trigo- nometric) polynomial symbols is studied. We give a necessary and sufficient condition using the zeros of the analytic polynomial induced by the Fourier coefficients of the symbol.

     

Kernels of Hankel operators and hyponormality of Toeplitz operators

We give a formula for and describe when . We explore the hyponormality of Toeplitz operators whose symbols are of circulant type and some more general types. In addition, we discuss formulas for and estimates of the rank of the self-commutator of a hyponormal Toeplitz operator. Received September 17, 1999 / Revised May 25, 2000 / Published online December 8, 2000     

Backward Extensions of Recursively Generated Weighted Shifts and Quadratic Hyponormality

Given the weight sequence for a subnormal recursively generated weighted shift on Hilbert space, one approach to the study of classes of operators weaker than subnormal has been to form a backward extension of the shift by prefixing weights to the sequence. We characterize positive quadratic hyponormality and revisit quadratic hyponormality of certain such backward extensions of arbitrary length, generalizing earlier results, and also show that a function apparently introduced as a matter of convenience for quadratic hyponormality actually captures considerable information about positive quadratic hyponormality.     

Criteria for positively quadratically hyponormal weighted shifts

For bounded linear operators on Hilbert space, positive quadratic hyponormality is a property strictly between subnormality and hyponormality and which is of use in exploring the gap between these more familiar properties. Recently several related positively quadratically hyponormal weighted shifts have been constructed. In this note we establish general criteria for the positive quadratic hyponormality of weighted shifts which easily yield the results for these examples and other such weighted shifts.