Noncommutative stationary processes
By: Rolf Gohm.
Series: Lecture notes in mathematics,; 1839; Lecture notes in mathematics (Springer-Verlag) ;; 1839.
Publisher: Springer
Published: 2004
Place of publication: Berlin; New York
Language: eng
Number of pages: 170
Subjects: Stationary processes; Noncommutative algebras
Description: Quantum probability and the theory of operator algebras are both concerned with the study of noncommutative dynamics. Focusing on stationary processes with discrete-time parameter, this book presents (without many prerequisites) some basic problems of interest to both fields, on topics including extensions and dilations of completely positive maps, Markov property and adaptedness, endomorphisms of operator algebras and the applications arising from the interplay of these themes. Much of the material is new, but many interesting questions are accessible even to the reader equipped only with basic knowledge of quantum probability and operator algebras.
Notes: Includes bibliographical references (p. [165]-168) and index.
Originally presented as the author's habilitation (Greifswald) under the title: Elements of a spatial theory for noncommutative stationary processes with discrete time index.