Open Access
Spring 2014 Baire classes of $L_{1}$-preduals and $C^{*}$-algebras
Pavel Ludvík, Jiří Spurný
Illinois J. Math. 58(1): 97-112 (Spring 2014). DOI: 10.1215/ijm/1427897169

Abstract

Let $X$ be a separable real or complex $L_{1}$-predual such that its dual unit ball $B_{X^{*}}$ has the set $\operatorname{ext}B_{X^{*}}$ of its extreme points of type $F_{\sigma}$. We identify intrinsic Baire classes of $X$ with the spaces of odd or homogeneous Baire functions on $\operatorname{ext}B_{X^{*}}$. Further, we answer a question of S. A. Argyros, G. Godefroy and H. P. Rosenthal by showing that there exists a separable $C^{*}$-algebra $X$ (the so-called CAR-algebra) for which the second intrinsic Baire class of $X^{**}$ does not coincide with the second Baire class of $X^{**}$.

Citation

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Pavel Ludvík. Jiří Spurný. "Baire classes of $L_{1}$-preduals and $C^{*}$-algebras." Illinois J. Math. 58 (1) 97 - 112, Spring 2014. https://doi.org/10.1215/ijm/1427897169

Information

Published: Spring 2014
First available in Project Euclid: 1 April 2015

zbMATH: 1323.46005
MathSciNet: MR3331842
Digital Object Identifier: 10.1215/ijm/1427897169

Subjects:
Primary: 26A21 , 46B25
Secondary: 46A55 , 46B04 , 46L05

Rights: Copyright © 2014 University of Illinois at Urbana-Champaign

Vol.58 • No. 1 • Spring 2014
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