Overview
- Treats both classical and recent results in ergodic theory from a modern analytic perspective
- Assumes no background in ergodic theory, while providing a review of basic results in functional analysis
- Provides a foundation for understanding recent applications of ergodic theory to combinatorics and number theory
Part of the book series: Graduate Texts in Mathematics (GTM, volume 272)
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Table of contents (21 chapters)
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Front Matter
Keywords
About this book
Topics include:
• an intuitive introduction to ergodic theory
• an introduction to the basic notions, constructions, and standard examples of topological dynamical systems
• Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem
• measure-preserving dynamical systems
• von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem
• strongly and weakly mixing systems
• an examination of notions of isomorphism for measure-preserving systems
• Markov operators, and the related concept of a factor of a measure preserving system
• compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition
• an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy)
Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory
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Authors and Affiliations
About the authors
Bibliographic Information
Book Title: Operator Theoretic Aspects of Ergodic Theory
Authors: Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel
Series Title: Graduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-3-319-16898-2
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Tanja Eisner, B�lint Farkas, Markus Haase, and Rainer Nagel 2015
Hardcover ISBN: 978-3-319-16897-5Published: 28 November 2015
Softcover ISBN: 978-3-319-37105-4Published: 23 August 2016
eBook ISBN: 978-3-319-16898-2Published: 18 November 2015
Series ISSN: 0072-5285
Series E-ISSN: 2197-5612
Edition Number: 1
Number of Pages: XVIII, 628
Topics: Dynamical Systems and Ergodic Theory, Operator Theory, Functional Analysis