Description
Book SynopsisThis 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 BeurlingLax 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 BrangesRovnyak 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 ide
Trade Review'Noncommutative Function-Theoretic Operator Theory and Applications by Ball and Bolotnikov is a comprehensive monograph by acknowledged experts in the fields of operator theory and function theory. It gives an account of a very active area of modern research, to which the authors themselves have been major contributors. The significant themes of the book include reproducing kernel Hilbert spaces (notably weighted Bergman spaces), Beurling-Lax theorems, and systems-theoretic ideas expressed in operator-theoretic terms. The work as a whole is presented in a multivariable noncommutative context, and thus extends classical work on Hardy-space function theory and related operator theory.' Jonathan Partington, University of Leeds
Table of Contents1. 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 ω-hypercontractive operator tuples; 9. Regular formal power series.
