Strong Limit Theorems in Noncommutative L2-Spaces / Edition 1

Strong Limit Theorems in Noncommutative L2-Spaces / Edition 1

by Ryszard Jajte
     
 

ISBN-10: 3540542140

ISBN-13: 9783540542148

Pub. Date: 08/23/1991

Publisher: Springer Berlin Heidelberg

The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master

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Overview

The noncommutative versions of fundamental classical results on the almost sure convergence in L2-spaces are discussed: individual ergodic theorems, strong laws of large numbers, theorems on convergence of orthogonal series, of martingales of powers of contractions etc. The proofs introduce new techniques in von Neumann algebras. The reader is assumed to master the fundamentals of functional analysis and probability. The book is written mainly for mathematicians and physicists familiar with probability theory and interested in applications of operator algebras to quantum statistical mechanics.

Product Details

ISBN-13:
9783540542148
Publisher:
Springer Berlin Heidelberg
Publication date:
08/23/1991
Series:
Lecture Notes in Mathematics Series, #1477
Edition description:
1991
Pages:
113
Product dimensions:
6.00(w) x 9.10(h) x 0.40(d)

Table of Contents

Almost sure convergence in noncommutative L2-spaces.- Individual ergodic theorems in L2 over a von neumann algebra.- Asymptotic formulae.- Convergence of iterates of contractions.- Convergence of orthogonal series and strong laws of large numbers.- Convergence of conditional expectations and martingales.- Miscellaneous results.

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