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

Emmanuele, G.

Arch. Math., Brno 34, No. 4, 417-425 (1998).

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

Keywords:

isomorphic properties; approximation properties; spaces of operators; projective tensor product; approximation property