Noncommutative function-theoretic operator theory and applications

by Ball, Joseph A.

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Title Statements

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

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"--

Edition Statements

Publication Date:©2022

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge, United Kingdom
Language:eng
Publication Date:©2022

The Physical Object

Description:1 online resource (x, 428 pages) : : illustrations.

Edition Identifiers

ISBN:9781009004305, 1009004301, 1009020102, 9781009020107
oclc:on1261772413
LC Classification:QA331
Dewey Decimal:515/.9

1. Introduction; 2. Formal Reproducing Kenel Hilbert Spaces; 3. Contractive multipliers; 4. Stein relations and observability range spaces; 5. Beurling-Lax theorems based on contractive multipliers; 6. Non-orthogonal Beurling-Lax representations; 7. Orthogonal Beurling-Lax representations; 8. Models for -hypercontractive operator tuples; 9. Regular formal power series.