On the essential norms of Toeplitz operators with continuous symbols

Toeplitz operators with special symbols

On the Toeplitz operators with piecewise continuous symbols on the Bergman space

The paper is devoted to the study of Toeplitz operators with piecewise continuous symbols. We clarify the geometric regularities of the behaviour of the essential spectrum of Toeplitz operators in dependence on their crucial data: the angles between jump curves of symbols at a boundary point of discontinuity and on the limit values reached by a symbol at that boundary point. We show then that t...

Hyponormality of Toeplitz Operators with Rational Symbols

In this article we introduce a notion of ‘division’ for rational functions and then give a criterion for hyponormality of Tg+f (f, g are rational functions) in the cases where g divides f . Furthermore we show that we may assume, without loss of generality, that g divides f when we consider the hyponormality of Tg+f .

Toeplitz Operators and Toeplitz Algebra with Symbols of Vanishing Oscillation

We study the C∗-algebra generated by Teoplitz operators with symbols of vanishing (mean) oscillation on the Bergman space of the unit ball. We show that the index calculation for Fredholm operators in this C∗-algebra can be easily and completely reduced to the classic case of Toeplitz operators with symbols that are continuous on the closed unit ball. Moreover, in addition to a number of other ...

Toeplitz Operators with Essentially Radial Symbols

For Topelitz operators with radial symbols on the disk, there are important results that characterize boundedness, compactness, and its relation to the Berezin transform. The notion of essentially radial symbol is a natural extension, in the context of multiply-connected domains, of the notion of radial symbol on the disk. In this paper we analyze the relationship between the boundary behavior ...