Strong limit theorems in noncommutative L2-spaces
By: Ryszard Jajte.
Series: Lecture notes in mathematics ;; 1477; Lecture notes in mathematics (Springer-Verlag) ;; 1477.
Publisher: Springer-Verlag
Published: 1991
Place of publication: Berlin; New York
Language: eng
Number of pages: 113
Subjects: Von Neumann algebras.; Limit theorems (Probability theory); Ergodic theory.
Description: 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.
Notes: Includes bibliographical references (p. [103]-111) and index.