## Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel's Operator Theoretic Aspects of Ergodic Theory (Graduate Texts PDF

By Tanja Eisner, Bálint Farkas, Markus Haase, Rainer Nagel

ISBN-10: 3319168983

ISBN-13: 9783319168982

Attractive contemporary effects by means of Host–Kra, Green–Tao, and others, spotlight the timeliness of this systematic advent to classical ergodic thought utilizing the instruments of operator concept. Assuming no past publicity to ergodic thought, this publication offers a latest origin for introductory classes on ergodic idea, specifically for college kids or researchers with an curiosity in practical research. whereas easy analytic notions and effects are reviewed in different appendices, extra complex operator theoretic issues are constructed intimately, even past their fast reference to ergodic conception. subsequently, the booklet can be compatible for complex or special-topic classes on sensible research with purposes to ergodic theory.

Topics include:

• an intuitive creation to ergodic theory

• an advent to the fundamental notions, buildings, and conventional 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 suggest Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem

• strongly and weakly blending systems

• an exam of notions of isomorphism for measure-preserving systems

• Markov operators, and the similar suggestion of an element of a degree keeping system

• compact teams and semigroups, and a strong instrument of their research, the Jacobs–de Leeuw–Glicksberg decomposition

• an advent to the spectral conception of dynamical platforms, the theorems of Furstenberg and Weiss on a number of recurrence, and purposes of dynamical structures to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence precept, theorems of Roth and Furstenberg–Sárközy)

Beyond its use within the lecture room, Operator Theoretic points of Ergodic conception can function a worthwhile starting place for doing learn on the intersection of ergodic idea and operator thought