Noncommutative function-theoretic operator theory and applications

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"--