Steinberg symbols modulo the trace class, holonomy, and limit theorems for Toeplitz determinants

Szego Limit Theorems for Toeplitz Operators on Compact Homogeneous Spaces

Let / be a real valued integrable function on a compact homogeneous space M = K\G and M¡ the operator of pointwise multiplication by /. The authors consider families of Toeplitz operators T¡P = PM¡P as P ranges over a net of orthogonal projections from L2(M) to finite dimensional G-invariant subspaces. Necessary and sufficient conditions are given on the net in order that the distribution of ei...

Class of Limit Theorems for Singular Diffusions

On the Limit of Some Toeplitz-Like Determinants

In this article we derive, using standard methods of Toeplitz theory, an asymptotic formula for certain large minors of Toeplitz matrices. Bump and Diaconis obtained the same asymptotics using representation theory, with an answer having a different form.

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 special symbols