Matrix functions of bounded type: an interplay between function theory and operator theory

著者

• Curto, Raúl E.
• Hwang, In Sung
• Yi, U-yŏng

書誌事項

Matrix functions of bounded type: an interplay between function theory and operator theory

Raúl E. Curto, In Sung Hwang, Woo Young Lee

（Memoirs of the American Mathematical Society, no. 1253）

American Mathematical Society, c2019

注記

"July 2019, volume 260, number 1253 (second of 5 numbers)"

Includes bibliographical reference

内容説明・目次

内容説明

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.

目次

Introduction Preliminaries Coprime inner functions Douglas-Shapiro-Shields factorizations Tensored-scalar singularity An interpolation problem and a functional calculus Abrahamse's theorem for matrix-valued symbols A subnormal Toeplitz completion Hyponormal Toeplitz pairs Concluding remarks Bibliography List of Symbols.

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詳細情報

• NII書誌ID(NCID): BB28991434
• ISBN:
  • 9781470436247
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, RI.
• ページ数/冊数: v, 100 p.
• 大きさ: 26 cm
• 親書誌ID:
  • BA00035927