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Descriptive properties of elements of biduals of Banach spaces

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Ludvík P., Spurný J.

Studia Mathematica

2012

tom 209

nr 1

71-99

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.

Ograniczanie wyników

1 Studia Mathematica

1 Ludvík P.

1 Spurný J.

1 2012

Wyniki wyszukiwania

Descriptive properties of elements of biduals of Banach spaces