Completely positive maps of order zero on pro-𝐶∗-algebras
نویسندگان
چکیده
منابع مشابه
Covariant Completely Positive Linear Maps between Locally C-algebras
We prove a covariant version of the KSGNS (Kasparov, Stinespring, Gel’fand,Naimark,Segal) construction for completely positive linear maps between locally C-algebras. As an application of this construction, we show that a covariant completely positive linear map ρ from a locally C-algebra A to another locally C -algebra B with respect to a locally C-dynamical system (G,A,α) extends to a complet...
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If A is a unital C∗-algebra and if H is a complex Hilbert space, then the set SH(A) of all unital completely positive linear maps from A to the algebra B(H) of continuous linear operators on H is an operator-valued, or generalised, state space of A. The usual state space of A occurs with the one-dimensional Hilbert space C. The structure of the extreme points of generalised state spaces was det...
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The order relation on the set of completely n-positive linear maps from a pro-C-algebra A to L(H), the C-algebra of bounded linear operators on a Hilbert space H, is characterized in terms of the representation associated with each completely n-positive linear map. Also, the pure elements in the set of all completely n-positive linear maps from A to L(H) and the extreme points in the set of uni...
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We said that φ is n-positive if φn is positive and that φ is completely positive if φn is positive for all n. The map φ is said to be n-bounded (resp., n-contractive) if ‖φn‖ ≤ c (resp., ‖φn‖ ≤ 1). The map φ is said to be completely bounded (resp., completely contractive) if ‖φ‖cb = supn‖φ‖n <∞ (resp., ‖φ‖cc = supn‖φn‖ ≤ 1). npositivity (resp., n-boundedness or n-contractivity) implies (n−1)-po...
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Let φ : Mn → B(H) be an injective, completely positive contraction with ‖φ−1 : φ(Mn) → Mn‖cb ≤ 1 + δ(ǫ). We show that if either (i) φ(Mn) is faithful modulo the compact operators or (ii) φ(Mn) approximately contains a rank 1 projection, then there is a complete order embedding ψ : Mn → B(H) with ‖φ − ψ‖cb < ǫ. We also give examples showing that such a perturbation does not exist in general. As ...
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ژورنال
عنوان ژورنال: Forum Mathematicum
سال: 2020
ISSN: 1435-5337,0933-7741
DOI: 10.1515/forum-2020-0012