Student Co-author

Pomona Undergraduate

Document Type

Article

Department

Mathematics (Pomona)

Publication Date

2012

Keywords

Toeplitz operator, model space, truncated Toeplitz operator, reproducing kernel, complex symmetric operator, conjugation, hyperbolic geometry, Euclid, Hilbert’s axioms, pseudo-hyperbolic metric, hyperbolic metric, Poincaré model, trace

Abstract

Unlike Toeplitz operators on H², truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this paper 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 ≤ 3 is unitarily equivalent to a direct sum of truncated Toeplitz operators.

Comments

First published in Proceedings of the American Mathematical Society in Volume 140, Number 4, April 2012, published by the American Mathematical Society.

Rights Information

© 2011 American Mathematical Society

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