Descriptive properties of elements of biduals of Banach spaces
Pavel Ludvík ; Jiří Spurný
Studia Mathematica, Tome 209 (2012), p. 71-99 / Harvested from The Polish Digital Mathematics Library

If E is a Banach space, any element x** in its bidual E** is an affine function on the dual unit ball BE* 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 BE*, 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.

Publié le : 2012-01-01
EUDML-ID : urn:eudml:doc:286365
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     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},
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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/