Descriptive properties of elements of biduals of Banach spaces

Pavel Ludvík; Jiří Spurný

Studia Mathematica (2012)

  • Volume: 209, Issue: 1, page 71-99
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Pavel Ludvík, and Jiří Spurný. "Descriptive properties of elements of biduals of Banach spaces." Studia Mathematica 209.1 (2012): 71-99. <http://eudml.org/doc/286365>.

@article{PavelLudvík2012,
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 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.},
author = {Pavel Ludvík, Jiří Spurný},
journal = {Studia Mathematica},
keywords = {Baire and Borel functions; strongly affine functions; fragmentable functions; extreme points; L1-preduals; Baire classes and intrinsic Baire classes of Banach spaces},
language = {eng},
number = {1},
pages = {71-99},
title = {Descriptive properties of elements of biduals of Banach spaces},
url = {http://eudml.org/doc/286365},
volume = {209},
year = {2012},
}

TY - JOUR
AU - Pavel Ludvík
AU - Jiří Spurný
TI - Descriptive properties of elements of biduals of Banach spaces
JO - Studia Mathematica
PY - 2012
VL - 209
IS - 1
SP - 71
EP - 99
AB - 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.
LA - eng
KW - Baire and Borel functions; strongly affine functions; fragmentable functions; extreme points; L1-preduals; Baire classes and intrinsic Baire classes of Banach spaces
UR - http://eudml.org/doc/286365
ER -

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