ERGODIC THEORY AND VON NEUMANN ALGEBRAS AN INTRODUCTION

ERGODIC THEORY AND VON NEUMANN ALGEBRAS : AN INTRODUCTION CLAIRE ANANTHARAMAN-DELAROCHE Contents 1. Finite von Neumann algebras : examples and some basics 2 1.1. Notation and preliminaries 2 1.2. Measure space von Neumann algebras 5 1.3. Group von Neumann algebras 5 1.4. Standard form 9 1.5. Group measure space von Neumann algebras 11 1.6. Von Neumann algebras from equivalence relations 16 1.7. Two non-isomorphic II1 factors 20 Exercises 23 2. About factors arising from equivalence relations 25 2.1. Isomorphisms of equivalence relations vs isomorphisms of their von Neumann algebras 25 2.2. Cartan subalgebras 25 2.3. An application: computation of fundamental groups 26 Exercise 27 3. Study of the inclusion L∞(T2) ? L∞(T2)o F2 29 3.1. The Haagerup property 30 3.2. Relative property (T) 31 References 35 1

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• hilbert space


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• topology