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Session 36. Topology in Functional Analysis
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Descriptive properties of elements of biduals of Banach spaces |
Jiří Spurný, Charles University, Czech Republic
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If \(E\) is a Banach space, any element \(x^{**}\) in its bidual \(E^{**}\) is an affine function on the dual unit ball \(B_{E^*}\) that might possess variety of descriptive properties with respect to the weak* topology. We prove several results showing that descriptive properties of \(x^{**}\) are quite often determined by the behaviour of \(x^{**}\) on the set of extreme points of \(B_{E^*}\), generalizing thus results of J. Saint Raymond and F. Jellett. We also prove a result on the relation between Baire classes and intrinsic Baire classes of \(L_1\)-preduals which were introduced by S.A. Argyros, G. Godefroy and H.P. Rosenthal.
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