Operator Theoretic Aspects of Ergodic Theory

Since its birth as a mathematical discipline, ergodic theory has had a strong operator theoretic flavor. This graduate text focuses on the interplay between ergodic theory and operator theory in hopes to foster new research that will lead to yet unknown connections between operator theory and ergodic theory in the future. Some recent applications of ergodic theory to combinatorial number theory use sophisticated operator theoretic constructions. On the other hand, results and problems from ergodic theory, once formulated in operator theoretic terms, inspired the development of functional analytic theories with stunning applications. This text develops the operator theory that is significant for or inspired by ergodic theory in a systematic and concise way. The reader is not expected to have any prior encounter with ergodic theory, so it can also serve as an introduction to ergodic theory from a functional analytic perspective. The book can be used for advanced master s and beginning doctoral level classes in the following areas: ergodic theory or dynamical systems with an emphasis on ergodic theorems; functional analysis or operator theory with applications to dynamical system theory; and semigroup methods in dynamical systems. It may also be used as a reference text by researchers in both ergodic and operator theory, and functional analysts who want to make their first steps in ergodic theory. Prerequisites include a familiarity with basic functional analysis, measure theory and topology, but the necessary background is collected in Appendices A-C.