Article - preprint
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.
© 2010 Indiana University Mathematics Journal
Cima, Joseph A.; Garcia, Stephan Ramon; Ross, William T.; and Wogen, Warren R., "Truncated Toeplitz Operators: Spatial Isomorphism, Unitary Equivalence, and Similarity" (2009). Pomona Faculty Publications and Research. 247.