Properties of mono-weakly hyponormal 2-variable weighted shifts

In this paper, we study several properties for mono-weakly hyponormal 2-variable weighted shifts. First, we consider propagation phenomena for mono-weakly hyponormal (resp. mono-polynomially hyponormal) 2-variable weighted shifts. Next, we contemplate the mono-weak hyponormality under the Schur product. Finally, we study whether the mono-weak hyponormality is invariant under powers.     

完全非正规Toeplitz算子

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.     

On totally *-paranormal operators

In this paper we study some properties of a totally *-paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally *-paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally *-paranormal operators through the local spectral theory. Finally, we show that every totally *-paranormal operator satisfies an analogue of the single valued extension property for W ²(D, H) and some of totally *-paranormal operators have scalar extensions.     

Inner derivations and norm equality

We characterize when the norm of the sum of two bounded operators on a Hilbert space is equal to the sum of their norms.

     

APPLICATION OF TWO OPERATORS TRANSFORM FROM CLASS A OPERATOR TO THE CLASS OF HYPONORMAL OPERATOR

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).     

Hyponormality of bounded‐type Toeplitz operators

In this paper we deal with the hyponormality of Toeplitz operators with matrix‐valued symbols. The aim of this paper is to provide a tractable criterion for the hyponormality of bounded‐type Toeplitz operators (i.e., the symbol is a matrix‐valued function such that Φ and are of bounded type). In particular, we get a much simpler criterion for the hyponormality of when the co‐analytic part of the symbol Φ is a left divisor of the analytic part.     

The essential selfcommutator of a subnormal operator

In this paper an easier proof is obtained of Alexandru Aleman's extension of an inequality of Axler and Shapiro for subnormal operators to the essential norm. The method is applied to show that a hyponormal operator whose essential spectrum has area zero must be essentially normal.

     

离散交换群上Toeplitz 算子的代数性质

广泛的意义下定义 Toeplitz 算子, 给出了Toeplitz 算子乘积仍为Toeplitz 算子的充分必要条件, Toeplitz算子是正规算子的充分必要条件以及 Toeplitz 算子可交换的一个必要条件,从而推广了经典 Toeplitz 算子的相应结果.     

Triangular Toeplitz contractions and Cowen sets for analytic polynomials

Let be the collection of lower triangular Toeplitz matrices and let be the collection of lower triangular Toeplitz contractions. We show that is compact and strictly convex, in the spectral norm, with respect to ; that is, is compact, convex and , where and denote the topological boundary with respect to and the set of extreme points, respectively. As an application, we show that the reduced Cowen set for an analytic polynomial is strictly convex; more precisely, if is an analytic polynomial and if hyponormal}\}$">, then is strictly convex. This answers a question of C. Cowen for the case of analytic polynomials.

     

算子的算子点谱的判定

本文讨论了算子Ａ∈Ｂ（Ｈ）_Ｎ为算子Ｔ∈Ｂ（Ｈ）的算子点谱的判定条件,特别得到：当Ｔ为亚正常算子时,Ａ为Ｔ的算子点谱的判定条件,另外还得到ｋｅｒτ^ｎ_Ｔ,Ａ＝ｋｅｒτ_Ｔ,Ａ成立的充分条件