Dynamics of linear operators
著者
書誌事項
Dynamics of linear operators
（Cambridge tracts in mathematics, 179）
Cambridge University Press, 2009
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注記
Includes bibliographical references (p. 321-330) and index
内容説明・目次
内容説明
The dynamics of linear operators is a young and rapidly evolving branch of functional analysis. In this book, which focuses on hypercyclicity and supercyclicity, the authors assemble the wide body of theory that has received much attention over the last fifteen years and present it for the first time in book form. Selected topics include various kinds of 'existence theorems', the role of connectedness in hypercyclicity, linear dynamics and ergodic theory, frequently hypercyclic and chaotic operators, hypercyclic subspaces, the angle criterion, universality of the Riemann zeta function, and an introduction to operators without non-trivial invariant subspaces. Many original results are included, along with important simplifications of proofs from the existing research literature, making this an invaluable guide for students of the subject. This book will be useful for researchers in operator theory, but also accessible to anyone with a reasonable background in functional analysis at the graduate level.
目次
- Introduction
- 1. Hypercyclic and supercyclic operators
- 2. Hypercyclicity everywhere
- 3. Connectedness and hypercyclicity
- 4. Weakly mixing operators
- 5. Ergodic theory and linear dynamics
- 6. Beyond hypercyclicity
- 7. Common hypercyclic vectors
- 8. Hypercyclic subspaces
- 9. Supercyclicity and the angle criterion
- 10. Linear dynamics and the weak topology
- 11. Universality of the Riemann zeta function
- 12. About 'the' Read operator
- Appendices
- Notations
- Index
- Bibliography.
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