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Points fixes dans les espaces des operateurs nucleaires

Published online by Cambridge University Press:  17 April 2009

Mourad Besbes
Mourad Besbes
Affiliation:
Equipe d'analyse, Boîte 186 Université Paris VI 4, Place Jussieu 75252 - Paris Cedex 05, France
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Abstract

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We prove that some metric inequalities imply weak or weak-star normal structure. In particular, we prove that every ω*-compact convex set in the space C1(lp, lq) of nuclear operators from lp into lq, (1 < p, q < ∞, 1/p + 1/q = 1) has the weak* normal structure. This generalises a recent result of C. Lennard.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 2 , October 1992 , pp. 287 - 294
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Arazy, A., ‘More on convergence in unitary matrix spaces’, Proc. Amer. Math. Soc. 83 (1981), 44–48.Google Scholar
[2]Besbes, M., ‘Points fixes des contractions définies sur un convexe L °-fermé de L 1’, C.R.A. Sciences de Paris, t. 311 (1990), 243–246.Google Scholar
[3]Besbes, M., Dilworth, S., Dowling, P. and Lennard, C., ‘New convexity and fixed point properties in Hardy and Lebesgue-Bochner spaces’, J. Fund. Anal, (to appear).Google Scholar
[4]Brodski, M.S. and Milman, D.P., ‘On the center of a convex set’, Dokl. Acad. Nauk. USSR 59 (1948), 837–840.Google Scholar
[5]Van Dulst, D., ‘Equivalent norms and the fixed point property for non-expansive mappings’, J. London Math. Soc. 25 (1982), 139–144.CrossRefGoogle Scholar
[6]Van Dulst, D. and Sims, B., ‘Fixed points of non-expansive mappings and Chebyshev centers in Banach spaces with norms of type (KK)’, in Lecture notes in Math. 991, pp. 34–43 (Springer-Verlag, Berlin, Heidelberg, New York, 1983).Google Scholar
[7]Gossez, J.P. and Dozo, E. Lami, ‘Normal structure and Schauder bases’, Acad. Roy. Belg. Bull. Cl. Sci. 55 (1969), 673–681.Google Scholar
[8]Khamsi, A., Thèse de doctorat (Université Paris VI, 1987).Google Scholar
[9]Khamsi, A., ‘Normal structure for Banach spaces with Schauder decomposition’, Canad. Math. Bull 32 (1989), 344–351.CrossRefGoogle Scholar
[10]Lennard, C., ‘C 1 is uniformly Kadec Klee*’, Proc. Amer. Math. Soc. 109 (1990), 71–77.Google Scholar
[11]Lennard, C., ‘A new convexity property that implies a fixed point property for L1’, (préprint).Google Scholar
[12]Lim, T.C., ‘Asymptotic centers and non-expansive mappings in conjugate Banach spaces’, Pacific J. Math. 90 (1980), 135–143.CrossRefGoogle Scholar
[13]Simon, B., ‘Convergence in trace ideals’, Proc. Amer. Math. Soc. 83 (1981), 39–43.CrossRefGoogle Scholar
[14]Sims, B., ‘Fixed points of non-expansive maps on weak and weak*-compact sets’, in Queen's University of Kingston. Lecture Notes, 1982.Google Scholar
[15]Swaminathan, S., ‘Normal structure in Banach spaces and its generalisations’, Contemp. Math. A.M.S. Providence 18, 201–215.Google Scholar
[16]Opial, Z., ‘Weak convergence of the sequence of successive approximations for non-expansive mappings’, Bull Amer. Math. Soc. 73 (1967), 591–597.Google Scholar