Descriptive properties of elements of biduals of Banach spaces

• Autorzy: Pavel Ludvík , Jiří Spurný
• Języki publikacji: EN

Abstrakty

EN

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 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 $B_{E*}$, 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 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.

Kategorie tematyczne

• 46B99: None of the above, but in this section
• 26A21: Classification of real functions; Baire classification of sets and functions
• 46A55: Convex sets in topological linear spaces; Choquet theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 209
• Numer: 1
• Strony: 71-99

Daty

wydano

2012

Twórcy

autor

Pavel Ludvík

• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

autor

Jiří Spurný

• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/sm209-1-6