Symbols of compact truncated Toeplitz operators

Bounded Symbols and Reproducing Kernel Thesis for Truncated Toeplitz Operators

Compressions of Toeplitz operators to coinvariant subspaces of H are called truncated Toeplitz operators. We study two questions related to these operators. The first, raised by Sarason, is whether boundedness of the operator implies the existence of a bounded symbol; the second is the Reproducing Kernel Thesis. We show that in general the answer to the first question is negative, and we exhibi...

Toeplitz operators with special symbols

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 ...

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 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 ...