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The uniform Kadec–Klee property for Orlicz–Lorentz spaces

Published online by Cambridge University Press:  01 September 2007

A. KAMIŃSKA ,
CHRIS LENNARD ,
MIECZYSŁAW MASTYŁO  and
SYLWIA MIKULSKA
A. KAMIŃSKA
Affiliation:
Department of Mathematical Sciences, The University of Memphis, Memphis, TN 38152, U.S.A. email: [email protected]
CHRIS LENNARD
Affiliation:
Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A. email: [email protected]
MIECZYSŁAW MASTYŁO
Affiliation:
Faculty of Mathematics and Computer Science, A. Mickiewicz University; and Institute of Mathematics, Polish Academy of Science (Poznań branch), Umultowska 87, 61-614 Poznań, Poland. email: [email protected]
SYLWIA MIKULSKA
Affiliation:
Institute of Mathematics, Szczecin University of Technology, Al. Piastów 48/49, 70-311 Szczecin, Poland. email: [email protected]
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Abstract

We give sufficient conditions, as well as some necessary conditions, for the Orlicz–Lorentz space Λϕ,ω to have the weak-star uniform Kadec–Klee property. These results generalize the characterization of the weak-star uniform Kadec–Klee property in the Lorentz space Λω = Lω,1 due to Dilworth and Hsu.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 349 - 374
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

REFERENCES

[1]Bennett, C. and Sharpley, R.. Interpolation of operators. Pure Appl. Math. 129 (Academic Press, 1988).Google Scholar
[2]Carothers, N. L., Dilworth, S. J., Lennard, C. J. and Trautman, D. A.. A fixed point property for the Lorentz space Lp,1. Indiana Univ. Math. J. 40 (1991), 345–352.CrossRefGoogle Scholar
[3]Dilworth, S. J. and Hsu, Yu-Ping. The uniform Kadec–Klee property for the Lorentz spaces Lw,1. J. Austral. Math. Soc. Ser A 60 (1996), 7–17.CrossRefGoogle Scholar
[4]Dilworth, S. J. and Lennard, C. J.. Uniform Kadec–Klee Lorentz spaces Lw,1 and uniformly concave functions. Canad. Math. Bulletin 39 (3) (1996), 266–274.CrossRefGoogle Scholar
[5]Dodds, P. G., Dodds, T. K., Dowling, P. N., Lennard, C. J. and Sukochev, F. A.. A uniform Kadec–Klee property for symmetric operator spaces. Math. Proc. Camb. Phil. Soc. 118 (1995), 487–502.CrossRefGoogle Scholar
[6]van Dulst, D. and Sims, B.. Fixed points of nonexpansive mappings and Chebyshev centers in Banach spaces with norms of type (KK). in: Banach Space Theory and its Applications (Proc Bucharest, 1981), Lecture Notes in Math. 991 (Springer, 1983), 35–43.CrossRefGoogle Scholar
[7]Dulst, D. van and de Valk, V.. (KK)-properties, normal structure and fixed points of nonexpansive mappings in Orlicz sequence spaces. Canad. J. Math. 38 (3) (1986), 728–750.CrossRefGoogle Scholar
[8]Hudzik, H., Kamińska, A. and Mastył, M.. On the dual of Orlicz–Lorentz space. Proc. Amer. Math. Soc. 130 (2002), 1645–1654.CrossRefGoogle Scholar
[9]Kalton, N. J., Peck, N. T. and Roberts, J. W.. An F-space Sampler. (Cambridge University Press, 1984).CrossRefGoogle Scholar
[10]Kamińska, A. and Mastył, M.. Duality and classical opearators in function spaces. Report No. 112/(2001), 30 pp., Faculty of Math. and Comp. Sci., Poznań.Google Scholar
[11]Kamińska, A.. Some remarks on Orlicz–Lorentz spaces. Math. Nachr. 147 (1990), 29–38.CrossRefGoogle Scholar
[12]Kamińska, A.. Uniform convexity of generalized Lorentz spaces. Arch. Math. 56 (1991), 181–188.CrossRefGoogle Scholar
[13]Kamińska, A., Maligranda, L. and Persson, L. E.. Convexity, concavity, type and cotype of Lorentz spaces. Indag. Math., N.S. 9 (3) (1998), 367–382.CrossRefGoogle Scholar
[14]Kantorovich, L. V. and Akilov, G. P.. Functional Analysis, 2nd rev. ed., “Nauka” (Moscow, 1997) (in Russian); (English transl., Pergamon Press, 1982).Google Scholar
[15]Kirk, W. A.. A fixed point theorem for mappings which do not increase distances. Amer. Math Monthly 72 (1965), 1004–1006.CrossRefGoogle Scholar
[16]Krasnoselskii, M. A. and Rutickii, Ya. B.. Convex Functions and Orlicz Spaces (Noordhoff Groningen, 1961).Google Scholar
[17]Krein, S. G., Petunin, Ju. I. and Semenov, E. M.. Interpolation of linear operators. Amer. Math. Soc. Trans. of Math. Monog. 54 (Providence, 1982).Google Scholar
[18]Lindenstrauss, J. and Tzafriri, L.. Classical Banach Spaces II (Springer-Verlag, 1979).CrossRefGoogle Scholar
[19]Natanson, I. P.. Theory of Functions of a Real Variable (Frederik Unger Publ. Co., 1995).Google Scholar
[20]Royden, H. L.. Real Analysis (MacMillan Publ. Co., 1988).Google Scholar