Descriptive properties of elements of biduals of Banach spaces

Details Descriptive properties of elements of biduals of Banach spaces Descriptive properties of elements of biduals of Banach spaces

2011-05-17

arxiv.org/abs/1105.3413v1

Mathematics

Functional Analysis

Scientific paper

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 several results on 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. Also, several examples witnessing natural limits of our positive results are presented.

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