Geodesic
Baire classes of complex $L_1$-preduals
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 3, pp. 659-676
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Let $X$ be a complex \mbox {$L_1$-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 \mbox {$\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).
Let $X$ be a complex \mbox {$L_1$-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 \mbox {$\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).
DOI : 10.1007/s10587-015-0201-6
Classification : 26A21, 46B20, 46B25
Keywords: complex $L_1$-predual; extreme point; Baire function 
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Ludvík, Pavel; Spurný, Jiří. Baire classes of complex $L_1$-preduals. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 3, pp. 659-676. doi: 10.1007/s10587-015-0201-6

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