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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)

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
Creator
Contributor
Author
Subject
Language
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 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
Member of
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)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-16898-2
Instantiates
Publication
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 -- 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
Control code
978-3-319-16898-2
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, non-commercial 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
10.1007/978-3-319-16898-2
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)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-16898-2
Publication
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 -- 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
Control code
978-3-319-16898-2
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, non-commercial 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
10.1007/978-3-319-16898-2
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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