2009/07/15 by Cima, Joseph A., Garcia, Stephan Ramon, Ross, William T. +1 · 1 citation
#47Bxx #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.0907.2489
A truncated Toeplitz operator is the compression Aϕ:\KΘ → \KΘ of a Toeplitz operator Tϕ:H2→ H2 to a model space \KΘ := H2 \ominus ΘH2. For Θ inner, let \TΘ denote the set of all bounded truncated Toeplitz operators on \KΘ. Our main result is a necessary and sufficient condition on inner functions Θ1 and Θ2 which guarantees that TΘ1 and TΘ2 are spatially isomorphic (i.e., U\TΘ1 = \TΘ2U for some unitary U:\KΘ1 → \KΘ2). 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.