Dynamics of Linear Operators

The first book to assemble the wide body of theory which has rapidly developed on the dynamics of linear operators.

Frédéric Bayart (Author), Étienne Matheron (Author)

9780521514965, Cambridge University Press

Hardback, published 4 June 2009

352 pages, 105 exercises
23.4 x 15.2 x 2.5 cm, 0.62 kg

'The beginning of each chapter sets the stage for what is to follow and each concludes with detailed comments, notes, references and a carefully selected list of problems. These serve the reader well, providing historical motivation as well as resources for further work … the book … is well developed, the material is well motivated and the selected topics that are explained include original results along with important simplifications of proofs from the existing research literature. The book has an extensive list of references covering the topics discussed, making it an excellent guide for students of the subject … this well-written book is a valuable resource for anyone working in Operator Theory, but is also accessible to anyone with a reasonable background in functional analysis at the graduate level.' Mathematical Reviews

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.

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.

Subject Areas: Functional analysis & transforms [PBKF]