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Anatomy of the C ∗-algebra generated by Toeplitz operators with piece-wise continuous symbols ∗

By Sergei Grudsky and Nikolai Vasilevski

Abstract

We study the structure of the C ∗-algebra generated by Toeplitz operators with piece-wise continuous symbols, putting a special emphasis to Toeplitz operators with unbounded symbols. We show that none of a finite sum of finite products of the initial generators is a compact perturbation of a Toeplitz operator. At the same time the uniform closure of the set of such sum of products contains a huge amount of Toeplitz operators with bounded and unbounded symbols drastically different from symbols of the initial generators.

Year: 2014
OAI identifier: oai:CiteSeerX.psu:10.1.1.417.7738
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