The Resource Operator Theoretic Aspects of Ergodic Theory, by Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel, (electronic resource)
Operator Theoretic Aspects of Ergodic Theory, by Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel, (electronic resource)
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The item Operator Theoretic Aspects of Ergodic Theory, by Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item Operator Theoretic Aspects of Ergodic Theory, by Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
 Summary
 Stunning recent results by HostKra, GreenTao, 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 GelfandNaimark 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 Jacobsde LeeuwGlicksberg 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 FurstenbergSárközy) 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
 Language
 eng
 Edition
 1st ed. 2015.
 Extent
 XVIII, 628 p. 25 illus., 1 illus. in color.
 Contents

 What is Ergodic Theory?
 Topological Dynamical Systems
 Minimality and Recurrence
 The C*algebra C(K) and the Koopman Operator
 MeasurePreserving 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 Jacobsde LeeuwGlicksberg Decomposition
 Dynamical Systems with Discrete Spectrum
 A Glimpse at Arithmetic Progressions
 Joinings
 The HostKra 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
 Isbn
 9783319168982
 Label
 Operator Theoretic Aspects of Ergodic Theory
 Title
 Operator Theoretic Aspects of Ergodic Theory
 Statement of responsibility
 by Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel
 Language
 eng
 Summary
 Stunning recent results by HostKra, GreenTao, 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 GelfandNaimark 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 Jacobsde LeeuwGlicksberg 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 FurstenbergSárközy) 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
 http://library.link/vocab/creatorName
 Eisner, Tanja
 Dewey number
 515.48
 Image bit depth
 0
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Farkas, Bálint.
 Haase, Markus.
 Nagel, Rainer.
 SpringerLink (Online service)
 Series statement
 Graduate Texts in Mathematics,
 Series volume
 272
 http://library.link/vocab/subjectName

 Mathematics
 Dynamics
 Ergodic theory
 Functional analysis
 Operator theory
 Label
 Operator Theoretic Aspects of Ergodic Theory, by Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 What is Ergodic Theory?  Topological Dynamical Systems  Minimality and Recurrence  The C*algebra C(K) and the Koopman Operator  MeasurePreserving 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 Jacobsde LeeuwGlicksberg Decomposition  Dynamical Systems with Discrete Spectrum  A Glimpse at Arithmetic Progressions  Joinings  The HostKra 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
 Control code
 9783319168982
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 XVIII, 628 p. 25 illus., 1 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319168982
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319168982
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086461328
 Label
 Operator Theoretic Aspects of Ergodic Theory, by Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel, (electronic resource)
 Antecedent source
 mixed
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier.
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent.
 Contents
 What is Ergodic Theory?  Topological Dynamical Systems  Minimality and Recurrence  The C*algebra C(K) and the Koopman Operator  MeasurePreserving 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 Jacobsde LeeuwGlicksberg Decomposition  Dynamical Systems with Discrete Spectrum  A Glimpse at Arithmetic Progressions  Joinings  The HostKra 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
 Control code
 9783319168982
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 XVIII, 628 p. 25 illus., 1 illus. in color.
 File format
 multiple file formats
 Form of item
 electronic
 Governing access note
 Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, noncommercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
 Isbn
 9783319168982
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia.
 Media type code

 c
 Other control number
 10.1007/9783319168982
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)1086461328
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.library.eui.eu/portal/OperatorTheoreticAspectsofErgodicTheoryby/1O6D9XDHtCc/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/OperatorTheoreticAspectsofErgodicTheoryby/1O6D9XDHtCc/">Operator Theoretic Aspects of Ergodic Theory, by Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>