03281nam 22006495 450 99646649930331620200701203823.03-540-39902-X10.1007/b95349(CKB)1000000000230990(SSID)ssj0000325204(PQKBManifestationID)12118373(PQKBTitleCode)TC0000325204(PQKBWorkID)10321396(PQKB)11769003(DE-He213)978-3-540-39902-5(MiAaPQ)EBC5592468(PPN)155226762(EXLCZ)99100000000023099020121227d2004 u| 0engurnn|008mamaatxtccrNoncommutative Stationary Processes[electronic resource] /by Rolf Gohm1st ed. 2004.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2004.1 online resource (VIII, 172 p.) Lecture Notes in Mathematics,0075-8434 ;1839Originally presented as the author's habilitation (Greifswald) under the title: Elements of a spatial theory for noncommutative stationary processes with discrete time index.3-540-20926-3 Includes bibliographical references (pages [165]-168) and index.Preface -- Introduction -- 1. Extensions and dilations -- 2. Markov processes -- 3. Adaptedness -- 4. Examples and applications -- A. Some facts about unital completely positive maps -- References -- Index.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.Lecture Notes in Mathematics,0075-8434 ;1839ProbabilitiesFunctional analysisOperator theoryProbability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Operator Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M12139Probabilities.Functional analysis.Operator theory.Probability Theory and Stochastic Processes.Functional Analysis.Operator Theory.519.232Gohm Rolfauthttp://id.loc.gov/vocabulary/relators/aut282339MiAaPQMiAaPQMiAaPQBOOK996466499303316Noncommutative stationary processes262659UNISA