On a question of Niels Grønbaek

Details On a question of Niels Grønbaek On a question of Niels Grønbaek

1999-08-11

arxiv.org/abs/math/9908049v1

Mathematics

Functional Analysis

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Scientific paper

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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