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Article - preprint


Mathematics (Pomona)

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truncated Toeplitz Operators, spatial isomorphism, unitary equivalence


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.


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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).

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