Matrix Functions of Bounded Type: An Interplay Between Function Theory and Operator Theory (Memoirs of the American Mathematical Society)

Raul E. Curto; in Sung Hwang; Woo Young Lee

ISBN 10: 1470436248 / ISBN 13: 9781470436247

Published by Amer Mathematical Society, 2019

Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less 0.47. Seller Inventory # G1470436248I3N00

Synopsis:

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.

About the Author: Raul E. Curto, University of Iowa, Iowa City.

In Sung Hwang, Sungkyunkwan University, Suwon, Korea.

Woo Young Lee, Seoul National University, Korea.

Bibliographic Details

Title: Matrix Functions of Bounded Type: An ...
Publisher: Amer Mathematical Society
Publication Date: 2019
Binding: Paperback
Condition: Good
Dust Jacket Condition: No Jacket