E0–Semigroups for Continuous Product Systems
نویسنده
چکیده
We show that every continuous product system of correspondences over a unital C∗–algebra occurs as the product system of a strictly continuous E0–semigroup.
منابع مشابه
E0–Semigroups for Continuous Poduct Systems: The Nonunital Case
Let B be a σ–unital C–algebra. We show that every strongly continuous E0–semigroup on the algebra of adjointable operators on a full Hilbert B–module E gives rise to a full continuous product system of correspondences over B. We show that every full continuous product system of correspondences over B arises in that way. If the product system is countably generated, then E can be chosen countabl...
متن کاملClassification of E0–Semigroups by Product Systems
In these notes we tie up some loose ends in the theory of E0–semigroups and their classification by product systems of Hilbert modules. We explain how the notion of cocycle conjugacy must be modified in order to see how product systems classify E0–semigroups. Actually, we will find two notions of cocycle conjugacy (which for Hilbert spaces coincide) that lead to classification up to isomorphism...
متن کاملOn the Existence of E0-semigroups
Product systems are the classifying structures for semigroups of endomorphisms of B(H), in that two E0-semigroups are cocycle conjugate iff their product systems are isomorphic. Thus it is important to know that every abstract product system is associated with an E0-semigrouop. This was first proved more than fifteen years ago by rather indirect methods. Recently, Skeide has given a more direct...
متن کاملPath spaces, continuous tensor products, and E0semigroups, Operator Algebras and Applications
We classify all continuous tensor product systems of Hilbert spaces which are “infinitely divisible” in the sense that they have an associated logarithmic structure. These results are applied to the theory of E0-semigroups to deduce that every E0-semigroup possessing sufficiently many “decomposable” operators must be cocycle conjugate to a CCR flow. A path space is an abstraction of the set of ...
متن کاملPath Spaces , Continuous Tensor Products
We classify all continuous tensor product systems of Hilbert spaces which are “infinitely divisible” in the sense that they have an associated logarithmic structure. These results are applied to the theory of E0-semigroups to deduce that every E0-semigroup possessing sufficiently many “decomposable” operators must be cocycle conjugate to a CCR flow. A path space is an abstraction of the set of ...
متن کامل