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Operator theoretic aspects of ergodic theory / Tanja Eisner...[et al.].

By: Contributor(s): Series: Graduate texts in mathematics ; 272.Publication details: Cham : Springer, 2015.Description: xviii, 628 p. : illustrations (some color) ; 24 cmISBN:
  • 9783319168975
Subject(s): DDC classification:
  • 515.48 23 Ei36
Contents:
1. What is Ergodic Theory? -- 2. Topological Dynamical Systems -- 3. Minimality and Recurrence -- 4. The C*-algebra C(K) and the Koopman Operator -- 5. Measure-Preserving Systems -- 6. Recurrence and Ergodicity -- 7. The Banach Lattice Lp and the Koopman Operator -- 8. The Mean Ergodic Theorem -- 9. Mixing Dynamical Systems -- 10. Mean Ergodic Operators on C(K) -- 11. The Pointwise Ergodic Theorem -- 12. Isomorphisms and Topological Models -- 13. Markov Operators -- 14. Compact Groups -- 15. Group actions and representations -- 16. The Jacobs?de Leeuw?Glicksberg Decomposition -- 17. The Kronecker Factor and Systems with Discrete Spectrum -- 18. The Spectral Theorem and Dynamical Systems -- 19. Topological Dynamics and Colorings -- 20. Arithmetic Progressions and Ergodic Theory -- 21. More Ergodic Theorems -- A: Topology -- B: Measure and Integration Theory.- C: Functional Analysis -- D: Operator Theory on Hilbert Spaces -- E: The Riesz Representation Theorem -- F: Standard Probability Spaces -- G: Theorems of Eberlein, Grothendieck, and Ellis -- Bibliography -- Index -- Symbol index.
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.
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Holdings
Item type Current library Call number Status Date due Barcode Item holds
Books ISI Library, Kolkata 515.48 Ei36 (Browse shelf(Opens below)) Available 136754
Total holds: 0

Includes bibliographical references and index.

1. What is Ergodic Theory? --
2. Topological Dynamical Systems --
3. Minimality and Recurrence --
4. The C*-algebra C(K) and the Koopman Operator --
5. Measure-Preserving Systems --
6. Recurrence and Ergodicity --
7. The Banach Lattice Lp and the Koopman Operator --
8. The Mean Ergodic Theorem --
9. Mixing Dynamical Systems --
10. Mean Ergodic Operators on C(K) --
11. The Pointwise Ergodic Theorem --
12. Isomorphisms and Topological Models --
13. Markov Operators --
14. Compact Groups --
15. Group actions and representations --
16. The Jacobs?de Leeuw?Glicksberg Decomposition --
17. The Kronecker Factor and Systems with Discrete Spectrum --
18. The Spectral Theorem and Dynamical Systems --
19. Topological Dynamics and Colorings --
20. Arithmetic Progressions and Ergodic Theory --
21. More Ergodic Theorems --
A: Topology --
B: Measure and Integration Theory.-
C: Functional Analysis --
D: Operator Theory on Hilbert Spaces --
E: The Riesz Representation Theorem --
F: Standard Probability Spaces --
G: Theorems of Eberlein, Grothendieck, and Ellis --
Bibliography --
Index --
Symbol index.

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.

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