Unitary equivalence to truncated Toeplitz operators

TL;DR

This paper characterizes operators unitarily equivalent to truncated Toeplitz operators, revealing they include sums of tensor products and inflations, thus broadening understanding of their structure and answering a specific open question.

Contribution

It demonstrates that the class of operators unitarily equivalent to truncated Toeplitz operators includes sums of tensor products and arbitrary inflations, expanding the known scope.

Findings

Contains sums of tensor products of truncated Toeplitz operators

Includes arbitrary inflations of truncated Toeplitz operators

Answers an open question by Cima et al.

Abstract

In this paper we investigate operators unitarily equivalent to truncated Toeplitz operators. We show that this class contains certain sums of tensor products of truncated Toeplitz operators. In particular, it contains arbitrary inflations of truncated Toeplitz operators; this answers a question posed by Cima, Garcia, Ross, and Wogen.