Document Type

Article - preprint

Department

Mathematics (Pomona)

Publication Date

2009

Keywords

truncated Toeplitz Operators, spatial isomorphism, unitary equivalence

Abstract

A truncated Toeplitz operator A φ : K Θ → K Θ is the compression of a Toeplitz operator T φ : H 2 → H 2 to a model space K Θ ≔ H 2 ⊖ Θ H 2 . For Θ inner, let T Θ denote the set of all bounded truncated Toeplitz operators on K Θ . Our main result is a necessary and sufficient condition on inner functions Θ 1 and Θ 2 which guarantees that T Θ 1 and T Θ 2 are spatially isomorphic (i.e., U T Θ 1 = T Θ 2 U for some unitary U : K Θ 1 → K Θ 2 ). We also study operators which are unitarily equivalent to truncated Toeplitz operators and we prove that every operator on a finite dimensional Hilbert space is similar to a truncated Toeplitz operator.

Comments

Pre-print from http://arxiv.org/abs/0907.2489

Final publication can be found at:

Cima, J.A., Garcia, S.R., Ross, W.T., Wogen, W.R., Truncated Toeplitz operators: spatial isomorphism, unitary equivalence, and similarity, Indiana Univ. Math. J., 59 (2010), 595–620. MR2648079 (2011i:47035). http://www.iumj.indiana.edu/oai/2010/59/4097/4097.xml

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© 2010 Indiana University Mathematics Journal

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