Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Formal Reproducing Kernel 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 Based on Wandering Subspaces
- 7 Orthogonal Beurling–Lax Representations Based on Wandering Subspaces
- 8 Models for ω-Hypercontractive Operator Tuples
- 9 Weighted Hardy–Fock Spaces Built from a Regular Formal Power Series
- References
- Notation Index
- Subject Index
4 - Stein Relations and Observability Range Spaces
Published online by Cambridge University Press: 09 December 2021
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Formal Reproducing Kernel 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 Based on Wandering Subspaces
- 7 Orthogonal Beurling–Lax Representations Based on Wandering Subspaces
- 8 Models for ω-Hypercontractive Operator Tuples
- 9 Weighted Hardy–Fock Spaces Built from a Regular Formal Power Series
- References
- Notation Index
- Subject Index
Summary
Chapter 4 is concerned with the state/output part of a noncommutative linear system and the range of the associated observability operator. Specifically, (i) observability operators having range landing inside of a given weighted Hardy–Fock space are characterized by the existence of a solution to certain Linear Matrix Inequality (Linear Operator Inequality in general) called a Stein inequality, (ii) conversely, subspaces of a given weighted Hardy–Fock space arising as the range of a contractive observability operator are characterized as contractively included backward-shift-invariant subspaces of the ambient Hardy–Fock space having some additional natural structural properties.
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- Publisher: Cambridge University PressPrint publication year: 2021