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James quasi reflexive space has the fixed point property. (English) Zbl 0672.47045
Using the works of Maurey and Lin, the author proves that the classical sequence James space J has the fixed point property. The main result states:
Every weakly compact convex subset of J has the fixed point property.
This gives rise to an example of a Banach space with a non-unconditional basis.
Reviewer: Shaligram Singh

MSC:
47H10 Fixed-point theorems
46B25 Classical Banach spaces in the general theory
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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References:
[1] Lin, Texas Functional Analysis Seminar 1982–1983
[2] Lin, Pacific J. Math. 116 pp 69– (1985) · Zbl 0566.47038
[3] DOI: 10.2307/2313345 · Zbl 0141.32402
[4] Kirk, Fixed point theory for non-expansive mapping I, II: Lecture Notes in Math 886 pp 484– (1981)
[5] Karlovitz, Pacific J. Math. 66 pp 153– (1976) · Zbl 0349.47043
[6] James, Studia. Math. 60 pp 157– (1977)
[7] DOI: 10.1073/pnas.37.3.174 · Zbl 0042.36102
[8] DOI: 10.1007/BF03007648 · Zbl 0344.46045
[9] DOI: 10.2307/1999928 · Zbl 0494.46014
[10] DOI: 10.1007/BF02762773 · Zbl 0461.46011
[11] DOI: 10.2307/2043954 · Zbl 0468.47036
[12] DOI: 10.2307/2318219 · Zbl 0336.47033
[13] Maurey, Points fixes des contractions sur un convexe ferme de L pp 80–
[14] Lindenstrauss, Classical Banach spaces I (1977)
[15] Lin, Bull. Inst. Math. Acad. Sinica 8 pp 389– (1980)
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