Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, and Similarity

By Joseph A. Cima, Stephan Ramon Garcia, William T. Ross, W. Wogen. 2009

76 citations recorded by the source corpus.

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 e ΘH 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 Θ1 and TΘ 2 are spatially isomorphic (i.e., UT Θ1 = T Θ2 U for some unitary U: K Θ1 → K Θ2 ). 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/205165fd9d5d32b8f83b97553324e763d94c95f3

Citations in the corpus

• Bounded symbols and Reproducing Kernel Thesis for truncated Toeplitz operators (2009, unknown): “As a basic reference for their main properties, [29] is invaluable; further study can be found in [9, 10, 18] and in [30, Section 7].”