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.
© 2011 American Mathematical Society
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.