Noncommutative function-theoretic operator theory and applications
Ball, Joseph A.
Noncommutative function-theoretic operator theory and applications by Joseph A. Ball and Vladimir Bolotnikov - New York : Cambridge Universirty Press, ©2022 - x, 428 p.; 25 cm. - Cambridge tracts in mathematics; 225 .
Includes bibliographical references and index.
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
"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"--
9781316518991
Hardy spaces.
Functions of complex variables.
MATHEMATICS / Algebra / Abstract
QA331 / .B24 2021
515.9 / BAL-N
Noncommutative function-theoretic operator theory and applications by Joseph A. Ball and Vladimir Bolotnikov - New York : Cambridge Universirty Press, ©2022 - x, 428 p.; 25 cm. - Cambridge tracts in mathematics; 225 .
Includes bibliographical references and index.
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
"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"--
9781316518991
Hardy spaces.
Functions of complex variables.
MATHEMATICS / Algebra / Abstract
QA331 / .B24 2021
515.9 / BAL-N