E0-SEMIGROUPS FOR CONTINUOUS PRODUCT SYSTEMS
نویسندگان
چکیده
منابع مشابه
E0–Semigroups for Continuous Product Systems
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.
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...
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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 کاملContinuous Families of E0-semigroups
We consider families of E0-semigroups continuously parametrized by a compact Hausdorff space, which are cocycle-equivalent to a given E0-semigroup β. When the gauge group of β is a Lie group, we establish a correspondence between such families and principal bundles whose structure group is the gauge group of β. Let H be a Hilbert space, which we will always assume to be separable and infinitedi...
متن کاملMinimal E0–semigroups
It is known that every semigroup of normal completely positive maps of a von Neumann can be “dilated” in a particular way to an E0-semigroup acting on a larger von Neumann algebra. The E0-semigroup is not uniquely determined by the completely positive semigroup; however, it is unique (up to conjugacy) provided that certain conditions of minimality are met. Minimality is a subtle property, and i...
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ژورنال
عنوان ژورنال: Infinite Dimensional Analysis, Quantum Probability and Related Topics
سال: 2007
ISSN: 0219-0257,1793-6306
DOI: 10.1142/s0219025707002774