This is an announcement for the paper "Descriptive properties of elements of biduals of Banach spaces" by Pavel Ludvik and Jiri Spurny.
Abstract: 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.
Archive classification: math.FA
Mathematics Subject Classification: 46B99, 46A55, 26A21
Submitted from: spurny@karlin.mff.cuni.cz
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1105.3413
or