Strong Limit Theorems in Noncommutative L2-Spaces
Jajte, Ryszard.
Strong Limit Theorems in Noncommutative L2-Spaces [electronic resource] / by Ryszard Jajte. - X, 113 p. online resource. - Lecture Notes in Mathematics, 1477 0075-8434 ; . - Lecture Notes in Mathematics, 1477 .
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.
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.
9783540475125
10.1007/BFb0098424 doi
Global analysis (Mathematics).
Distribution (Probability theory.
Analysis.
Probability Theory and Stochastic Processes.
Theoretical, Mathematical and Computational Physics.
QA299.6-433
515
Strong Limit Theorems in Noncommutative L2-Spaces [electronic resource] / by Ryszard Jajte. - X, 113 p. online resource. - Lecture Notes in Mathematics, 1477 0075-8434 ; . - Lecture Notes in Mathematics, 1477 .
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.
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.
9783540475125
10.1007/BFb0098424 doi
Global analysis (Mathematics).
Distribution (Probability theory.
Analysis.
Probability Theory and Stochastic Processes.
Theoretical, Mathematical and Computational Physics.
QA299.6-433
515