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.

Bibliographic Information

Book Title: Strong Limit Theorems in Noncommutative L2-Spaces
Authors: Ryszard Jajte
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/BFb0098424
Publisher: Springer Berlin, Heidelberg
eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 1991
Softcover ISBN: 978-3-540-54214-8Published: 26 July 1991
eBook ISBN: 978-3-540-47512-5Published: 08 December 2006
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 113
Topics: Analysis, Probability Theory and Stochastic Processes, Theoretical, Mathematical and Computational Physics

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Strong Limit Theorems in Noncommutative L2-Spaces

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Table of contents (7 chapters)

Front Matter

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

Back Matter

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