zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the decomposition of quantum quadratic stochastic processes into layer-Markov processes defined on von Neumann algebras. (English. Russian original) Zbl 1074.46046
Summary: We give an expansion of a quantum quadratic stochastic process (q.q.s.p.) into a so-called fibrewise Markov process and prove that conversely, such an expansion uniquely determines the quantum quadratic stochastic process. As an application, we give a criterion (in terms of this expansion) for the q.q.s.p. to satisfy the ergodic principle. Using this result, we prove that a q.q.s.p. satisfies the ergodic principle if and only if the associated Markov process satisfies this principle. The expansion obtained is used to introduce a new notion of conjugacy of two q.q.s.p.’s and to study the relation between this notion and the ergodic principle.

46L53Noncommutative probability and statistics
46L55Noncommutative dynamical systems
46L60Applications of selfadjoint operator algebras to physics
46N50Applications of functional analysis in quantum physics
60G07General theory of stochastic processes
81S25Quantum stochastic calculus
Full Text: DOI