Student Co-author

Pomona Undergraduate

Document Type



Mathematics (Pomona)

Publication Date



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


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.


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

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© 2011 American Mathematical Society

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