## Some remarks on the equality $$W(E,F^\ast) = K(E,F^\ast)$$.(English)Zbl 0970.46011

Summary: We show that the equality $$W(E,F^\ast) = K(E, F^\ast)$$ is a necessary condition for the validity of certain results about isomorphic properties in the projective tensor product $$E \otimes _\pi F$$ of two Banach spaces under some approximation property type assumptions.

### MSC:

 46B28 Spaces of operators; tensor products; approximation properties 46B20 Geometry and structure of normed linear spaces 46B03 Isomorphic theory (including renorming) of Banach spaces
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