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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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