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.
Copyright © 2012 American Mathematical Society. This article first appeared in Proceedings of the American Mathematical Society 140:4 (2012), 1281-1295.
The definitive version is available at: http://www.ams.org/journals/proc/2012-140-04/home.html
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.
Ross, William T.; Garcia, Stephan Ramon; and Poore, Daniel E., "Unitary Equivalence to a Truncated Toeplitz Operator: Analytic Symbols" (2012). Math and Computer Science Faculty Publications. 17.