LEADER 05306nam 22007215 450 001 9910300256403321 005 20230216041804.0 010 $a3-319-16898-3 024 7 $a10.1007/978-3-319-16898-2 035 $a(CKB)3710000000521683 035 $a(SSID)ssj0001585392 035 $a(PQKBManifestationID)16265268 035 $a(PQKBTitleCode)TC0001585392 035 $a(PQKBWorkID)14864465 035 $a(PQKB)10891794 035 $a(DE-He213)978-3-319-16898-2 035 $a(MiAaPQ)EBC6313184 035 $a(MiAaPQ)EBC5591647 035 $a(Au-PeEL)EBL5591647 035 $a(OCoLC)932002578 035 $a(PPN)190532033 035 $a(EXLCZ)993710000000521683 100 $a20151118d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aOperator Theoretic Aspects of Ergodic Theory /$fby Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (XVIII, 628 p. 25 illus., 1 illus. in color.) 225 1 $aGraduate Texts in Mathematics,$x2197-5612 ;$v272 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-16897-5 320 $aIncludes bibliographical references and index. 327 $aWhat 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. 330 $aStunning recent results by Host?Kra, Green?Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: ?an intuitive introduction to ergodic theory ?an introduction to the basic notions, constructions, and standard examples of topological dynamical systems ?Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand?Naimark theorem ?measure-preserving dynamical systems ?von Neumann?s Mean Ergodic Theorem and Birkhoff?s Pointwise Ergodic Theorem ?strongly and weakly mixing systems ?an examination of notions of isomorphism for measure-preserving systems ?Markov operators, and the related concept of a factor of a measure-preserving system ?compact groups and semigroups, and a powerful tool in their study, the Jacobs?de Leeuw?Glicksberg decomposition ?an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai, and Hindman, Furstenberg?s Correspondence Principle, theorems of Roth and Furstenberg?Sárközy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory. 410 0$aGraduate Texts in Mathematics,$x2197-5612 ;$v272 606 $aDynamical systems 606 $aOperator theory 606 $aFunctional analysis 606 $aDynamical Systems 606 $aOperator Theory 606 $aFunctional Analysis 615 0$aDynamical systems. 615 0$aOperator theory. 615 0$aFunctional analysis. 615 14$aDynamical Systems. 615 24$aOperator Theory. 615 24$aFunctional Analysis. 676 $a515.42 700 $aEisner$b Tanja$4aut$4http://id.loc.gov/vocabulary/relators/aut$0508569 702 $aFarkas$b Bálint$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aHaase$b Markus$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aNagel$b Rainer$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300256403321 996 $aOperator Theoretic Aspects of Ergodic Theory$92523026 997 $aUNINA