Ebook: Strong Limit Theorems in Noncommutative L2-Spaces

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.

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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.

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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.
Content:
Front Matter....Pages -
Almost sure convergence in noncommutative L2-spaces....Pages 1-9
Individual ergodic theorems in L2 over a von neumann algebra....Pages 10-36
Asymptotic formulae....Pages 37-51
Convergence of iterates of contractions....Pages 52-63
Convergence of orthogonal series and strong laws of large numbers....Pages 64-84
Convergence of conditional expectations and martingales....Pages 85-89
Miscellaneous results....Pages 90-99
Back Matter....Pages -

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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.
Content:
Front Matter....Pages -
Almost sure convergence in noncommutative L2-spaces....Pages 1-9
Individual ergodic theorems in L2 over a von neumann algebra....Pages 10-36
Asymptotic formulae....Pages 37-51
Convergence of iterates of contractions....Pages 52-63
Convergence of orthogonal series and strong laws of large numbers....Pages 64-84
Convergence of conditional expectations and martingales....Pages 85-89
Miscellaneous results....Pages 90-99
Back Matter....Pages -
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