Operator Algebras and their Connections with Topology and Ergodic Theory, Huzihiro Araki; G. Arsene; Calvin C. Moore; Serban

Автор: Tanja Eisner; B?lint Farkas; Markus Haase; Rainer
Название: Operator Theoretic Aspects of Ergodic Theory
ISBN: 3319371053 ISBN-13(EAN): 9783319371054
Издательство: Springer
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Описание: 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.

Автор: Eisner Tanja
Название: Operator Theoretic Aspects of Ergodic Theory
ISBN: 3319168975 ISBN-13(EAN): 9783319168975
Издательство: Springer
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Цена: 65210.00 T
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Описание: 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-S rk zy)
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

Автор: Masamichi Takesaki
Название: Theory of Operator Algebras III
ISBN: 3642076882 ISBN-13(EAN): 9783642076886
Издательство: Springer
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Цена: 135090.00 T
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Описание: From the reviews: "These three bulky volumes [EMS 124, 125, 127] [...] provide an introduction to this rapidly developing theory. [...] These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Acta Scientiarum Mathematicarum

Автор: M. Am?lia Bastos; Amarino Lebre; Stefan Samko; Ily
Название: Operator Theory, Operator Algebras and Applications
ISBN: 3034808151 ISBN-13(EAN): 9783034808156
Издательство: Springer
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Цена: 111790.00 T
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Описание: This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens;

Автор: Manfred M?ller; Vyacheslav Pivovarchik
Название: Spectral Theory of Operator Pencils, Hermite-Biehler Functions, and their Applications
ISBN: 3319375679 ISBN-13(EAN): 9783319375670
Издательство: Springer
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Цена: 88500.00 T
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Описание: The theoretical part of this monograph examines the distribution of the spectrum of operator polynomials, focusing on quadratic operator polynomials with discrete spectra.

Автор: Takesaki, Masamichi
Название: Theory of operator algebras ii
ISBN: 3642076890 ISBN-13(EAN): 9783642076893
Издательство: Springer
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Цена: 135090.00 T
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Описание: Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis.

Название: Ergodic theory.
ISBN: 3319498452 ISBN-13(EAN): 9783319498454
Издательство: Springer
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Цена: 111790.00 T
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Описание: This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. The more advanced material includes Popa`s cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy. The structure of the book is designed to be flexible enough to serve a variety of readers.

Автор: P G Romeo; John. C Meakin; A R Rajan
Название: Semigroups, Algebras and Operator Theory
ISBN: 8132224876 ISBN-13(EAN): 9788132224877
Издательство: Springer
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Цена: 121110.00 T
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Описание: This book discusses recent developments in semigroup theory and its applications in areas such as operator algebras, operator approximations and category theory.

Автор: Stanley Eigen; Arshag Hajian; Yuji Ito; Vidhu Pras
Название: Weakly Wandering Sequences in Ergodic Theory
ISBN: 4431564004 ISBN-13(EAN): 9784431564003
Издательство: Springer
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Цена: 79190.00 T
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Описание: In time it was shown that ww and related sequences reflected significant and deep properties of ergodic transformations that preserve an infinite measure.This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinite measure.