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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...

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