Noncommutative function-theoretic operator theory and applications
"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-shif…
Read More ↓Title Statements
- Full title :Noncommutative function-theoretic operator theory and applications / Joseph A. Ball (Virginia Tech) and Vladimir Bolotnikov (William & Mary).
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"
Read More ↓Edition Statements
- Publication Date:2022
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:2022
Notes
Literaturverzeichnis Seite 415-424.
The Physical Object
- Description:x, 428 Seiten : Illustrationen
Edition Identifiers
- ISBN:9781316518991, 131651899X
- DOI:10.1017/9781009004305
- oclc:on1277030848
- LC Classification:QA331
- Dewey Decimal:515/.9
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