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 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 < 3 is unitarily equivalent to a direct sum of truncated Toeplitz operators.

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Copyright © 2012 American Mathematical Society. This article first appeared in Proceedings of the American Mathematical Society 140:4 (2012), 1281-1295.

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DOI: 10.1090/S0002-9939-2011-11060-8

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Garcia, Stephan Ramon, Daniel E. Poore, and William T. Ross. "Unitary Equivalence to a Truncated Toeplitz Operator: Analytic Symbols."Proceedings of the American Mathematical Society 140, no. 4 (2012): 1281-295. doi:10.1090/S0002-9939-2011-11060-8.

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