On Compactness in L...(..., X) in the Weak Topology and in the Topology ...(L...(..., X), L...(..., X')).

Jürgen Batt; Wolfgang Hiermeyer

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Throughout [this paper], E and F will denote Banach spaces. The bounded weak topology on a Banach space E, noted bw(E) or simply bw, is defined as the finest topology that agrees with the weak topology on bounded sets. It is proved in [3] that bw(E) is a locally convex topology if and only if E is reflexive. In this paper we introduce the compact weak topology on a Banach space E, noted kw(E) or simply kw, as the finest topology that agrees with the weak topology on weakly...