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)
$E_0$-semigroups for continuous product systems: the nonunital case. (English) Zbl 1193.46043
Summary: Let $\cal B$ be a $\sigma$-unital $C^*$-algebra. We show that every strongly continuous $E_0$-semigroup on the algebra of adjointable operators on a full Hilbert $\cal B$-module $E$ gives rise to a full continuous product system of correspondences over $\cal B$. We show that every full continuous product system of correspondences over $\cal B$ arises in that way. If the product system is countably generated, then $E$ can be chosen countably generated, and if $E$ is countably generated, then so is the product system. We show that under these countability hypotheses there is a one-to-one correspondence between $E_0$-semigroups up to stable cocycle conjugacy and continuous product systems up to isomorphism. This generalizes the results for unital $\cal B$ to the $\sigma $-unital case.

46L55Noncommutative dynamical systems
46L53Noncommutative probability and statistics
Full Text: EMIS EuDML arXiv