| Title:
|
Characterizations of $L^1$-predual spaces by centerable subsets (English) |
| Author:
|
Duan, Yanzheng |
| Author:
|
Lin, Bor-Luh |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2007 |
| Pages:
|
239-243 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note, we prove that a real or complex Banach space $X$ is an $L^1$-predual space if and only if every four-point subset of $X$ is centerable. The real case sharpens Rao's result in [{\it Chebyshev centers and centerable sets\/}, Proc. Amer. Math. Soc. {\bf 130} (2002), no. 9, 2593--2598] and the complex case is closely related to the characterizations of $L^1$-predual spaces by Lima [{\it Complex Banach spaces whose duals are $L_1$-spaces\/}, Israel J. Math. {\bf 24} (1976), no. 1, 59--72]. (English) |
| Keyword:
|
Chebyshev radius |
| Keyword:
|
centerable subsets and $L^1 $-predual spaces |
| MSC:
|
41A65 |
| MSC:
|
46B20 |
| idZBL:
|
Zbl 1199.41181 |
| idMR:
|
MR2338092 |
| . |
| Date available:
|
2009-05-05T17:02:36Z |
| Last updated:
|
2012-05-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119654 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[10] Rao T.S.S.R.K.: Chebyshev centers and centerable sets.Proc. Amer. Math. Soc. 130 (2002), 9 2593-2598. MR 1900866 |
| . |
