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arXiv · 1012.4820

Unitary equivalence to a truncated Toeplitz operator: analytic symbols

Stephan Ramon Garcia·Daniel E. Poore·William T. Ross
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Abstract

Unlike Toeplitz operators on $H^2$, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is constructive and we illustrate it with several examples. As a byproduct, we also prove that every complex symmetric operator on a Hilbert space of dimension $\leq 3$ is unitarily equivalent to a direct sum of truncated Toeplitz operators.

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Stephan Ramon Garcia, Daniel E. Poore, William T. Ross. 2010-12-21. Unitary equivalence to a truncated Toeplitz operator: analytic symbols. https://arxiv.org/abs/1012.4820

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