| Title:
|
Baire classes of complex $L_1$-preduals (English) |
| Author:
|
Ludvík, Pavel |
| Author:
|
Spurný, Jiří |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
3 |
| Year:
|
2015 |
| Pages:
|
659-676 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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). (English) |
| Keyword:
|
complex $L_1$-predual |
| Keyword:
|
extreme point |
| Keyword:
|
Baire function |
| MSC:
|
26A21 |
| MSC:
|
46B20 |
| MSC:
|
46B25 |
| idZBL:
|
Zbl 06537685 |
| idMR:
|
MR3407598 |
| DOI:
|
10.1007/s10587-015-0201-6 |
| . |
| Date available:
|
2015-10-04T18:07:25Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144436 |
| . |
| Reference:
|
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