If E is a Banach space, any element x** in its bidual E** is an affine function on the dual unit ball that might possess a 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 , 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 L₁-preduals which were introduced by S. A. Argyros, G. Godefroy and H. P. Rosenthal (2003). Also, several examples witnessing natural limits of our positive results are presented.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-1-6,
author = {Pavel Ludv\'\i k and Ji\v r\'\i\ Spurn\'y},
title = {Descriptive properties of elements of biduals of Banach spaces},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {71-99},
zbl = {06025372},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-1-6}
}
Pavel Ludvík; Jiří Spurný. Descriptive properties of elements of biduals of Banach spaces. Studia Mathematica, Tome 209 (2012) pp. 71-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-1-6/