Special Toeplitz operators on a class of bounded Hartogs domains

Index Theory for Toeplitz Operators on Bounded Symmetric Domains

In this note we give an index theory for Toeplitz operators on the Hardy space of the Shilov boundary of an arbitrary bounded symmetric domain. Our results generalize earlier work of Gohberg-Krein and Venugopalkrishna [12] for domains of rank 1 and of Berger-Coburn-Koranyi [1] for domains of rank 2. Bounded symmetric domains (Cartan domains, classical or exceptional) are the natural higher-dime...

Toeplitz operators with special symbols

Hyponormality of Bounded-Type Toeplitz Operators

In this paper we deal with the hyponormality of Toeplitz operators with matrixvalued symbols. The aim of this paper is to provide a tractable criterion for the hyponormality of bounded-type Toeplitz operators TΦ (i.e., the symbol Φ ∈ L ∞ Mn is a matrix-valued function such that Φ and Φ∗ are of bounded type). In particular, we get a much simpler criterion for the hyponormality of TΦ when the co-...

Bounded Berezin-toeplitz Operators on the Segal-bargmann Space

We discuss the boundedness of Berezin-Toeplitz operators on a generalized Segal-Bargmann space (Fock space) over the complex n-space. This space is characterized by the image of a global Bargmanntype transform introduced by Sjöstrand. We also obtain the deformation estimates of the composition of Berezin-Toeplitz operators whose symbols and their derivatives up to order three are in the Wiener ...

Toeplitz Operators and Related Function Algebras on Certain Pseudoconvex Domains

Toeplitz operators are defined on pseudoconvex domains in C and their spectral properties are studied. In addition, the linear space HTM + C is discussed and is seen to be a closed algebra on a variety of domains.