Baire classes of complex L 1 -preduals

Pavel Ludvík; Jiří Spurný

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 3, page 659-676
  • ISSN: 0011-4642

Abstract

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Let X be a complex L 1 -predual, non-separable in general. We investigate extendability of complex-valued bounded homogeneous Baire- α functions on the set ext B X * of the extreme points of the dual unit ball B X * to the whole unit ball B X * . As a corollary we show that, given α [ 1 , ω 1 ) , the intrinsic α -th Baire class of X can be identified with the space of bounded homogeneous Baire- α functions on the set ext B X * when ext B X * satisfies certain topological assumptions. The paper is intended to be a complex counterpart to the same authors’ paper: Baire classes of non-separable L 1 -preduals (2015). As such it generalizes former work of Lindenstrauss and Wulbert (1969), Jellett (1985), and ourselves (2014), (2015).

How to cite

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Ludvík, Pavel, and Spurný, Jiří. "Baire classes of complex $L_1$-preduals." Czechoslovak Mathematical Journal 65.3 (2015): 659-676. <http://eudml.org/doc/271809>.

@article{Ludvík2015,
abstract = {Let $X$ be a complex $L_1$-predual, non-separable in general. We investigate extendability of complex-valued bounded homogeneous Baire-$\alpha $ functions on the set $\mathop \{\rm ext\} B_\{X^*\}$ of the extreme points of the dual unit ball $B_\{X^*\}$ to the whole unit ball $B_\{X^*\}$. As a corollary we show that, given $\alpha \in [1,\omega _1)$, the intrinsic $\alpha $-th Baire class of $X$ can be identified with the space of bounded homogeneous Baire-$\alpha $ functions on the set $\mathop \{\rm ext\} B_\{X^*\}$ when $\mathop \{\rm ext\} B_\{X^*\}$ satisfies certain topological assumptions. The paper is intended to be a complex counterpart to the same authors’ paper: Baire classes of non-separable $L_1$-preduals (2015). As such it generalizes former work of Lindenstrauss and Wulbert (1969), Jellett (1985), and ourselves (2014), (2015).},
author = {Ludvík, Pavel, Spurný, Jiří},
journal = {Czechoslovak Mathematical Journal},
keywords = {complex $L_1$-predual; extreme point; Baire function},
language = {eng},
number = {3},
pages = {659-676},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Baire classes of complex $L_1$-preduals},
url = {http://eudml.org/doc/271809},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Ludvík, Pavel
AU - Spurný, Jiří
TI - Baire classes of complex $L_1$-preduals
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 3
SP - 659
EP - 676
AB - Let $X$ be a complex $L_1$-predual, non-separable in general. We investigate extendability of complex-valued bounded homogeneous Baire-$\alpha $ functions on the set $\mathop {\rm ext} B_{X^*}$ of the extreme points of the dual unit ball $B_{X^*}$ to the whole unit ball $B_{X^*}$. As a corollary we show that, given $\alpha \in [1,\omega _1)$, the intrinsic $\alpha $-th Baire class of $X$ can be identified with the space of bounded homogeneous Baire-$\alpha $ functions on the set $\mathop {\rm ext} B_{X^*}$ when $\mathop {\rm ext} B_{X^*}$ satisfies certain topological assumptions. The paper is intended to be a complex counterpart to the same authors’ paper: Baire classes of non-separable $L_1$-preduals (2015). As such it generalizes former work of Lindenstrauss and Wulbert (1969), Jellett (1985), and ourselves (2014), (2015).
LA - eng
KW - complex $L_1$-predual; extreme point; Baire function
UR - http://eudml.org/doc/271809
ER -

References

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