منابع مشابه
The Choquet Boundary of an Operator System
We show that every operator system (and hence every unital operator algebra) has sufficiently many boundary representations to generate the C*-envelope. We solve a 45 year old problem of William Arveson that is central to his approach to non-commutative dilation theory. We show that every operator system and every unital operator algebra has sufficiently many boundary representations to complet...
متن کاملThe Noncommutative Choquet Boundary
Let S be an operator system – a self-adjoint linear subspace of a unital C∗-algebra A such that 1 ∈ S and A = C∗(S) is generated by S. A boundary representation for S is an irreducible representation π of C∗(S) on a Hilbert space with the property that π S has a unique completely positive extension to C∗(S). The set ∂S of all (unitary equivalence classes of) boundary representations is the nonc...
متن کاملThe Noncommutative Choquet Boundary Ii: Hyperrigidity
A (finite or countably infinite) set G of generators of an abstract C∗-algebra A is called hyperrigid if for every faithful representation of A on a Hilbert space A ⊆ B(H) and every sequence of unital completely positive linear maps φ1, φ2, . . . from B(H) to itself, lim n→∞ ‖φn(g)− g‖ = 0,∀g ∈ G =⇒ lim n→∞ ‖φn(a)− a‖ = 0, ∀a ∈ A. We show that one can determine whether a given set G of generato...
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چکیده ندارد.
15 صفحه اولAsymptotic distribution of eigenvalues of the elliptic operator system
Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2015
ISSN: 0012-7094
DOI: 10.1215/00127094-3165004