Noncommutative function-theoretic operator theory and applications / Joseph A. Ball, Vladimir Bolotnikov.

Format:

Book

Author/Creator:

Ball, Joseph A., 1947- author.

Bolotnikov, Vladimir, 1962- author.

Series:

Cambridge tracts in mathematics

Language:

English

Subjects (All):

Hardy spaces.

Functions of complex variables.

Physical Description:

x, 428 pages : illustrations ; 24 cm.

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2022.

Summary:

"This concise monograph explores how core ideas in Hardy -space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system -theory ideas and reproducing -kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling-Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspacesubspaces form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges-Rovnyak model theory and characteristic operator function for a Hilbert -space contraction operator. The chapters that follow generalize the system theory and reproducing -kernel techniques to enable an extension of the ideas above to weighted Bergman -space multivariable settings"-- Provided by publisher.

Notes:

Includes bibliographical references and indexes.

Other Format:

Online version: Ball, Joseph A., 1947- Noncommutative function-theoretic operator theory and applications

ISBN:

9781316518991

131651899X

OCLC:

1251501633