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Conditions equivalent to C* independence

Shuilin Jin, Li Xu, Qinghua Jiang, Li Li (2012)

Studia Mathematica

Let and be mutually commuting unital C* subalgebras of (). It is shown that and are C* independent if and only if for all natural numbers n, m, for all n-tuples A = (A₁, ..., Aₙ) of doubly commuting nonzero operators of and m-tuples B = (B₁, ..., Bₘ) of doubly commuting nonzero operators of , S p ( A , B ) = S p ( A ) × S p ( B ) , where Sp denotes the joint Taylor spectrum.

Finite rank approximation and semidiscreteness for linear operators

Christian Le Merdy (1999)

Annales de l'institut Fourier

Given a completely bounded map u : Z M from an operator space Z into a von Neumann algebra (or merely a unital dual algebra) M , we define u to be C -semidiscrete if for any operator algebra A , the tensor operator I A u is bounded from A min Z into A nor M , with norm less than C . We investigate this property and characterize it by suitable approximation properties, thus generalizing the Choi-Effros characterization of semidiscrete von Neumann algebras. Our work is an extension of some recent work of Pisier on an analogous...

Tensor product construction of 2-freeness

R. Lenczewski (1998)

Banach Center Publications

From a sequence of m-fold tensor product constructions that give a hierarchy of freeness indexed by natural numbers m we examine in detail the first non-trivial case corresponding to m=2 which we call 2-freeness. We show that in this case the constructed tensor product of states agrees with the conditionally free product for correlations of order ≤ 4. We also show how to associate with 2-freeness a cocommutative *-bialgebra.

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