Operator Theoretic Aspects of Ergodic Theory

• Main Authors: Eisner, Tanja (Author), Farkas, Bálint (Author), Haase, Markus (Author), Nagel, Rainer (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Edition: 1st ed. 2015.
• Series: Graduate Texts in Mathematics, 272
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Functional analysis.; Operator theory.; Dynamical Systems and Ergodic Theory.; Operator Theory.; Functional Analysis.

Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodi...

Table of Contents:

• What is Ergodic Theory?
• Topological Dynamical Systems
• Minimality and Recurrence
• The C*-algebra C(K) and the Koopman Operator
• Measure-Preserving Systems
• Recurrence and Ergodicity
• The Banach Lattice Lp and the Koopman Operator
• The Mean Ergodic Theorem
• Mixing Dynamical Systems
• Mean Ergodic Operators on C(K)
• The Pointwise Ergodic Theorem
• Isomorphisms and Topological Models
• Markov Operators
• Compact Semigroups and Groups
• Topological Dynamics Revisited
• The Jacobs–de Leeuw–Glicksberg Decomposition
• Dynamical Systems with Discrete Spectrum
• A Glimpse at Arithmetic Progressions
• Joinings
• The Host–Kra– Tao Theorem
• More Ergodic Theorems
• Appendix A: Topology
• Appendix B: Measure and Integration Theory.- Appendix C: Functional Analysis
• Appendix D: The Riesz Representation Theorem
• Appendix E: Theorems of Eberlein, Grothendieck, and Ellis.