Brown–Halmos characterization of multi-Toeplitz operators associated with noncommutative polyhyperballs

Properties of Iteration of Toeplitz Operators with Toeplitz

We consider the problems of preconditioning and iterative inversion of Toeplitz operators on sequences of complex numbers. We divide the preconditioned operator into two parts, of which one is compact and the other is regarded as a small perturbation. It will be shown that the Krylov subspace methods (such as GMRES) will perform initially at superlinear speed when applied to such preconditioned...

Toeplitz Operators

This article discusses Paul Halmos’s crucial work on Toeplitz operators and the consequences of that work. Mathematics Subject Classification (2000). 47B35.

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 ...

Toeplitz Operators and Localization Operators

We show that for any localization operator on the Fock space with polynomial window, there exists a constant coefficient linear partial differential operator D such that the localization operator with symbol f coincides with the Toeplitz operator with symbol Df . An analogous result also holds in the context of Bergman spaces on bounded symmetric domains. This verifies a recent conjecture of Co...