Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory

Raul E. Curto

ISBN 10: 1470436248 / ISBN 13: 9781470436247

Verlag: American Mathematical Society, 2019

Beschreibung

2019. Paperback. . . . . . Bestandsnummer des Verkäufers V9781470436247

Bibliografische Details

Titel: Matrix Functions of Bounded Type: An ...

Verlag: American Mathematical Society

Erscheinungsdatum: 2019

Einband: Softcover

Zustand: New

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In this paper, the authors study matrix functions of bounded type from the viewpoint of describing an interplay between function theory and operator theory. They first establish a criterion on the coprime-ness of two singular inner functions and obtain several properties of the Douglas-Shapiro-Shields factorizations of matrix functions of bounded type. They propose a new notion of tensored-scalar singularity, and then answer questions on Hankel operators with matrix-valued bounded type symbols. They also examine an interpolation problem related to a certain functional equation on matrix functions of bounded type; this can be seen as an extension of the classical Hermite-Fejer Interpolation Problem for matrix rational functions. The authors then extend the $H^\infty$-functional calculus to an $\overline{H^\infty}+H^\infty$-functional calculus for the compressions of the shift. Next, the authors consider the subnormality of Toeplitz operators with matrix-valued bounded type symbols and, in particular, the matrix-valued version of Halmos's Problem 5 and then establish a matrix-valued version of Abrahamse's Theorem. They also solve a subnormal Toeplitz completion problem of $2\times 2$ partial block Toeplitz matrices. Further, they establish a characterization of hyponormal Toeplitz pairs with matrix-valued bounded type symbols and then derive rank formulae for the self-commutators of hyponormal Toeplitz pairs.