On the Existence of E0-semigroups
نویسنده
چکیده
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 proof. In this note we give yet another proof by a very simple construction.
منابع مشابه
2 3 M ay 2 00 7 GENERALIZED CCR FLOWS
We introduce a new construction of E0-semigroups, called generalized CCR flows, with two kinds of descriptions: those arising from sum systems and those arising from pairs of C0-semigroups. We get a new necessary and sufficient condition for them to be of type III, when the associated sum system is of finite index. Using this criterion, we construct examples of type III E0-semigroups, which can...
متن کاملThe Index of a Quantum Dynamical Semigroup
A numerical index is introduced for semigroups of completely positive maps of B(H) which generalizes the index of E0-semigroups. It is shown that the index of a unital completely positive semigroup agrees with the index of its dilation to an E0-semigroup, provided that the dilation is minimal. Introduction. We introduce a numerical index for semigroups P = {Pt : t ≥ 0} of normal completely posi...
متن کاملE0-dilation of strongly commuting CP0-semigroups
We prove that every strongly commuting pair of CP0-semigroups has a minimal E0-dilation. This is achieved in two major steps, interesting in themselves: 1: we show that a strongly commuting pair of CP0semigroups can be represented via a two parameter product system representation; 2: we prove that every fully coisometric product system representation has a fully coisometric, isometric dilation....
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 کاملOn Type Ii0 E0-semigroups Induced by Boundary Weight Doubles
Powers has shown that each spatial E0-semigroup can be obtained from the boundary weight map of a CP -flow acting on B(K ⊗ L(0,∞)) for some separable Hilbert space K. In this paper, we define boundary weight maps through boundary weight doubles (φ, ν), where φ : Mn(C) → Mn(C) is a q-positive map and ν is a boundary weight over L(0,∞). These doubles induce CP -flows over K for 1 < dim(K) < ∞ whi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006