Operator Theoretic Aspects of Ergodic Theory
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The work Operator Theoretic Aspects of Ergodic Theory represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Operator Theoretic Aspects of Ergodic Theory
Resource Information
The work Operator Theoretic Aspects of Ergodic Theory represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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 Operator Theoretic Aspects of Ergodic Theory
 Statement of responsibility
 by Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel
 Language

 eng
 eng
 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 specialtopic 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 •measurepreserving 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 measurepreserving systems •Markov operators, and the related concept of a factor of a measurepreserving 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
 Dewey number

 515.39
 515.48
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

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 Image bit depth
 0
 Language note
 English
 LC call number
 QA313
 Literary form
 non fiction
 Series statement
 Graduate Texts in Mathematics,
 Series volume
 272
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