Operator theoretic aspects of ergodic theory /

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Bibliographic Details
Imprint:	Cham : Springer, 2015.
Description:	1 online resource.
Language:	English
Series:	Graduate Texts in Mathematics, 0072-5285 ; 272 Graduate texts in mathematics ; 272.
Subject:	Ergodic theory. Ergodic theory.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11096763

Hidden Bibliographic Details
Other authors / contributors:	Eisner, Tanja, author. Farkas, Blint, author. Haase, Markus, 1970- author. Nagel, R. (Rainer), author.
ISBN:	9783319168982 3319168983 9783319168975 3319168975
Digital file characteristics:	text file PDF
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (SpringerLink, viewed December 23, 2015).
Summary:	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 ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. 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.
Other form:	Original 3319168975 9783319168975
Standard no.:	10.1007/978-3-319-16898-2

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.

Operator theoretic aspects of ergodic theory /

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