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.
Rights Information
© 2011 American Mathematical Society
Terms of Use & License Information
Recommended Citation
Garcia, S.R., Poore, D.E., Ross, W.T., Unitary equivalence to a truncated Toeplitz operator: analytic symbols, Proc. Amer. Math. Soc. 140 (2012), no. 4, 1281–1295. MR2869112.
Comments
First published in Proceedings of the American Mathematical Society in Volume 140, Number 4, April 2012, published by the American Mathematical Society.