Abstract:Abstract.A bounded linear operator is said to be nice if its adjoint preserves extreme points of the dual unit ball. Motivated by a description due to Labuschagne and Mascioni [9] of such maps for the space of compact operators on a Hilbert space, in this article we consider a description of nice surjections on K (X,Y ) for Banach spaces X,Y . We give necessary and sufficient conditions when nice surjections are given by composition operators. Our results imply automatic continuity of these maps with respect t… Show more
G-spaces are a class of L 1 -preduals introduced by Grothendieck. We prove that if every extreme operator from any Banach space into a G-space, X , is a nice operator (that is, its adjoint preserves extreme points), then X is isometrically isomorphic to c 0 (I ) for some set I . One of the main points in the proof is a characterization of spaces of type c 0 (I ) by means of the structure topology on the extreme points of the dual space.
G-spaces are a class of L 1 -preduals introduced by Grothendieck. We prove that if every extreme operator from any Banach space into a G-space, X , is a nice operator (that is, its adjoint preserves extreme points), then X is isometrically isomorphic to c 0 (I ) for some set I . One of the main points in the proof is a characterization of spaces of type c 0 (I ) by means of the structure topology on the extreme points of the dual space.
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