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In this paper, we study the matrix representations of compressions of Toeplitz operators to the finite dimensional model spaces H 2 BH 2 , where B is a finite Blaschke product. In particular, we determine necessary and sufficient conditions-in terms of the matrix representation-of when a linear transformation on H 2 BH 2 is the compression of a Toeplitz(More)
A truncated Toeplitz operator Aϕ : K Θ → K Θ is the compression of a Toeplitz operator Tϕ : H 2 → H 2 to a model space K Θ := H 2 ⊖ 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 Θ 1 and T Θ 2 are(More)
Unlike Toeplitz operators on H 2 , truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct eigenvalues to be unitarily equivalent to a truncated Toeplitz operator having an analytic symbol. This test is(More)
In this expository paper, we wish to survey both past and current work on the space of Cauchy transforms on the unit circle. By this we mean the collection K of analytic functions on the open unit disk D = {z ∈ C : |z| < 1} that take the form (1.1) (Kµ)(z) := dµ(ζ) 1 − ζz , where µ is a finite, complex, Borel measure on the unit circle T = ∂D. Our(More)