Abstract
We study in this paper properties of Schur multipliers of Schatten von Neumann classes Sp. We prove that for p≤1, Schur multipliers of Sp are necessarily completely bounded.We also introduce for p≤1 a scale Wp of tensor products of ℓ∞ and prove that matrices in Wp are Schur multipliers of Sp. We compare this sufficient condition with the sufficient condition of membership in the p-tensor product of ℓ∞ spaces.
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