Positive forms and dilations
نویسندگان
چکیده
منابع مشابه
Completely positive quantum stochastic convolution cocycles and their dilations
Stochastic generators of completely positive and contractive quantum stochastic convolution cocycles on a C∗-hyperbialgebra are characterised. The characterisation is used to obtain dilations and stochastic forms of Stinespring decomposition for completely positive convolution cocycles on a C∗-bialgebra. Stochastic (or Markovian) cocycles on operator algebras are basic objects of interest in qu...
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It is known that every semigroup of normal completely positive maps P = {Pt : t ≥ 0} of B(H), satisfying Pt(1) = 1 for every t ≥ 0, has a minimal dilation to an E0-semigroup acting on B(K) for some Hilbert space K ⊇ H. The minimal dilation of P is unique up to conjugacy. In a previous paper a numerical index was introduced for semigroups of completely positive maps and it was shown that the ind...
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It is well known that contractive representations of the disk algebra are completely contractive. Let A denote the subalgebra of the disk algebra consisting of those functions f for which f ′(0) = 0. We prove that there are contractive representations of A which are not completely contractive, and furthermore characterize those contractive representations which are completely contractive.
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The first representation theorem establishes a correspondence between positive, self-adjoint operators and closed, positive forms on Hilbert spaces. The aim of this paper is to show that some of the results remain true if the underlying space is a reflexive Banach space. In particular, the construction of the Friedrichs extension and the form sum of positive operators can be carried over to thi...
متن کاملPositive forms on hyperkähler manifolds
Let (M, I, J,K, g) be a hyperkähler manifold, dimR M = 4n. We study positive, ∂-closed (2p, 0)-forms on (M, I). These forms are quaternionic analogues of the positive (p, p)-forms, well-known in complex geometry. We construct a monomorphism Vp,p : Λ I (M)−→ Λ n+p,n+p I (M), which maps ∂-closed (2p, 0)-forms to closed (n+p, n+p)-forms, and positive (2p, 0)forms to positive (n + p, n + p)-forms. ...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1987
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1987-0882714-0