Symmetric and self-adjoint Toeplitz operators on multiply connected plane domains

Toeplitz Operators in Multiply Connected Regions

Counterexamples to Rational Dilation on Symmetric Multiply Connected Domains

We show that if R is a compact domain in the complex plane with two or more holes and an anticonformal involution onto itself (or equivalently a hyperelliptic Schottky double), then there is an operator T which has R as a spectral set, but does not dilate to a normal operator with spectrum on the boundary of R. 0.1. Definitions. LetX be a compact, path connected subset ofC, with interior R, and...

On subnormal operators whose spectrum are multiply connected domains

Let Ω be a connected bounded domain with a finite amount of “holes” and “nice boundary”. We study subnormal operators with spectrum equal to Ω, while the spectrum of their normal extensions are supported on the boundary, ∂Ω.

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...

Self-adjoint Difference Operators and Symmetric Al-salam–chihara Polynomials

The symmetric Al-Salam–Chihara polynomials for q > 1 are associated with an indeterminate moment problem. There is a self-adjoint second order difference operator on l(Z) to which these polynomials are eigenfunctions. We determine the spectral decomposition of this self-adjoint operator. This leads to a class of discrete orthogonality measures, which have been obtained previously by Christianse...