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The Weak* Karlovitz lemma for dual lattices

Published online by Cambridge University Press:  17 April 2009

Brailey Sims
Brailey Sims
Affiliation:
Deaprtment of Mathematics, The University of Newcastle, New South Wales 2308, Australia
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Abstract

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We establish the Karlovitz lemma for a nonexpansive self mapping of a nonempty weak* compact convex set in a weak* orthogonal dual Banach lattice.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 1 , February 1992 , pp. 171 - 176
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Borwein, J. and Sims, B., ‘Non-expansive mappings on Banach lattices and related topics’, Houston J. Math. 10 (1984), 339–355.Google Scholar
[2]Brodskii, M.S. and Mil'man, D.P., ‘On the center of a convex set’, Dokl. Akad. Nauk. SSSR 59 (1948), 837–840.Google Scholar
[3]Garkavi, A.L., ‘The best possible net and the best possible cross-section of a set in a normed linear space’, Amer. Math. Soc. Trans. Ser. 2 39 (1964), 111–131.Google Scholar
[4]Goebel, K., ‘On the structure of minimal invariant sets for nonexpansive mapings’, Ann. Univ. Mariae Curie-Sktodowska Sect A (Lublin) 9 (1975), 73–77.Google Scholar
[5]Karlovitz, L.A., ‘Existence of fixed points of nonexpansive mappings in a space without normal structure’, Pacific J. Math. 66 (1976), 153–159.CrossRefGoogle Scholar
[6]Khamsi, M.A., ‘On the weak*-fixed point property’, Contemp. Math. 85 (1989), 325–337.CrossRefGoogle Scholar
[7]Kirk, W.A., ‘A fixed point theorem for mappings which do not increase distances’, Amer. Math. Monthly 72 (1965), 1004–1006.CrossRefGoogle Scholar
[8]Lin, P-K., ‘Unconditional bases and fixed points of nonexpansive mappings’, Pacific J. Math. 116 (1985), 69–76.CrossRefGoogle Scholar
[9]Maurey, B., ‘Seminaire d'Analyse Fonctionnelle’, Exposé No. VIII (1980).Google Scholar
[10]Sims, B., ‘Orthogonality and fixed points of nonexpansive maps’, Proc. Centre Math. Anal. Aust. Nat. Uni. 20 (1988), 178–186.Google Scholar
[11]Soardi, P., ‘Existence of fixed points of nonexpansive mappings in certain Banach lattices’, Proc. Amer. Math. Soc. 73 (1979), 25–29.CrossRefGoogle Scholar