Strong Limit Theorems in Noncommutative L2-Spaces. 1st ed. 1991

種類:

電子ブック

責任表示:

by Ryszard Jajte

出版情報:

Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1991

著者名:

• Jajte, Ryszard.
• SpringerLink (Online service)

シリーズ名:

Lecture Notes in Mathematics ; 1477

ISBN:

9783540475125 [3540475125]    

注記:

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.

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