Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-28T20:15:46.313Z Has data issue: false hasContentIssue false

The Weak* Karlovitz lemma for dual lattices

Published online by Cambridge University Press:  17 April 2009

Brailey Sims
Affiliation:
Deaprtment of Mathematics, The University of Newcastle, New South Wales 2308, Australia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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
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), 339355.Google Scholar
[2]Brodskii, M.S. and Mil'man, D.P., ‘On the center of a convex set’, Dokl. Akad. Nauk. SSSR 59 (1948), 837840.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), 111131.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), 7377.Google Scholar
[5]Karlovitz, L.A., ‘Existence of fixed points of nonexpansive mappings in a space without normal structure’, Pacific J. Math. 66 (1976), 153159.CrossRefGoogle Scholar
[6]Khamsi, M.A., ‘On the weak*-fixed point property’, Contemp. Math. 85 (1989), 325337.CrossRefGoogle Scholar
[7]Kirk, W.A., ‘A fixed point theorem for mappings which do not increase distances’, Amer. Math. Monthly 72 (1965), 10041006.CrossRefGoogle Scholar
[8]Lin, P-K., ‘Unconditional bases and fixed points of nonexpansive mappings’, Pacific J. Math. 116 (1985), 6976.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), 178186.Google Scholar
[11]Soardi, P., ‘Existence of fixed points of nonexpansive mappings in certain Banach lattices’, Proc. Amer. Math. Soc. 73 (1979), 2529.CrossRefGoogle Scholar