| Title:
|
The fixed point property in a Banach space isomorphic to $c_0$ (English) |
| Author:
|
Poulios, Costas |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2014 |
| Pages:
|
195-202 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a Banach space, which comes naturally from $c_0$ and it appears in the literature, and we prove that this space has the fixed point property for non-expansive mappings defined on weakly compact, convex sets. (English) |
| Keyword:
|
non-expansive mappings |
| Keyword:
|
fixed point property |
| Keyword:
|
Banach spaces isomorphic to $c_0$ |
| MSC:
|
46B25 |
| MSC:
|
47H09 |
| MSC:
|
47H10 |
| idZBL:
|
Zbl 06391537 |
| idMR:
|
MR3193925 |
| . |
| Date available:
|
2014-06-07T15:33:53Z |
| Last updated:
|
2016-07-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143801 |
| . |
| Reference:
|
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| Reference:
|
[2] Argyros S.A., Deliyanni I., Tolias A.G.: Hereditarily indecomposable Banach Algebras of diagonal operators.Israel J. Math. 181 (2011), 65–110. Zbl 1219.46013, MR 2773038, 10.1007/s11856-011-0004-x |
| Reference:
|
[3] Browder F.E.: Nonexpansive nonlinear operators in Banach spaces.Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041–1044. MR 0187120, 10.1073/pnas.54.4.1041 |
| Reference:
|
[4] Elton J., Lin P., Odell E., Szarek S.: Remarks on the fixed point problem for nonexpansive maps.Contemporary Math. 18 (1983), 87–119. Zbl 0528.47040, MR 0728595, 10.1090/conm/018/728595 |
| Reference:
|
[5] Hagler J.: A counterexample to several questions about Banach spaces.Studia Math. 60 (1977), 289–308. Zbl 0387.46015, MR 0442651 |
| Reference:
|
[6] Karlovitz L.A.: Existence of fixed points for nonexpansive mappings in a space without normal structure.Pacific J. Math. 66 (1976), 153–159. MR 0435951, 10.2140/pjm.1976.66.153 |
| Reference:
|
[7] Kirk W.A.: A fixed point theorem for mappings which do not increase distances.Amer. Math. Monthly 72 (1965), 1004–1006. Zbl 0141.32402, MR 0189009, 10.2307/2313345 |
| Reference:
|
[8] Maurey B.: Points fixes des contractions sur un convexe forme de $L^1$.Seminaire d' Analyse Fonctionelle 80–81, Ecole Polytechnique, Palaiseau, 1981. MR 0659309 |
| . |
