On a question of Niels Grønbaek

Abstract

Let F(X) denote the norm closure of the space of all finite rank operators on a Banach space X. We show that there are Banach spaces X for which the product map $a\otimes b\to ab$ does not define a surjective map from the projective tensor product $F(X)\hat{\otimes }F(X)$ onto F(X).

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Cited by in corpus (1)

• Factorization and weak amenability of A(X)