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Noncommutative Function-Theoretic Operator Theory and Applications

Noncommutative Function-Theoretic Operator Theory and Applications

Noncommutative Function-Theoretic Operator Theory and Applications
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Noncommutative Function-Theoretic Operator Theory and Applications Hardback - 2021

by Joseph A. Ball and Vladimir Bolotnikov

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  • Title Noncommutative Function-Theoretic Operator Theory and Applications
  • Author Joseph A. Ball and Vladimir Bolotnikov
  • Binding Hardback
  • Condition New
  • Pages 440
  • Volumes 1
  • Language ENG
  • Publisher Cambridge University Press
  • Publication date 2021-12-16
  • Features Bibliography, Index
  • Bookseller's Inventory # 43109695
  • ISBN 9781316518991 / 131651899X
  • Weight 1.79 lbs (0.81 kg)
  • Dimensions 9 x 6 x 1.13 in (22.86 x 15.24 x 2.87 cm)
  • Category Mathematics
  • Library of Congress subjects Functions of complex variables, Hardy spaces
  • Library of Congress Catalogue Number 2021024660
  • Dewey Decimal Code 515.9
  • Quantity available 5

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From the publisher

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 subspace 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.

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