Operator Theoretic Aspects of Ergodic Theory

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 ergodi...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Eisner, Tanja (Autor), Farkas, Bálint (Autor), Haase, Markus (Autor), Nagel, Rainer (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cham : Springer International Publishing : Imprint: Springer, 2015.
Edición:1st ed. 2015.
Colección:Graduate Texts in Mathematics, 272
Temas:
Dynamical systems.
Operator theory.
Functional analysis.
Dynamical Systems.
Operator Theory.
Functional Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

Ejemplares similares