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1992 | 103 | 1 | 79-97
Tytuł artykułu

Points fixes et théorèmes ergodiques dans les espaces L¹(E)

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Abstrakty
EN
We prove that for each linear contraction T : X → X (∥T∥ ≤ 1), the subspace F = {x ∈ X : Tx = x} of fixed points is 1-complemented, where X is a suitable subspace of L¹(E*) and E* is a separable dual space such that the weak and weak* topologies coincide on the unit sphere. We also prove some related fixed point results.
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Twórcy
  • Equipe d'Analyse, Université Paris VI, Boîte 186, 4, Place Jussieu, F-75252 Paris Cedex 05, France
Bibliografia
  • [Als] D. Alspach, A fixed point free nonexpansive map, Proc. Amer. Math. Soc. 82 (1981), 423-424.
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  • [Bal.3] E. J. Balder, New sequential compactness results for spaces of scalarly integrable functions, J. Math. Anal. Appl. 151 (1990), 1-16.
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  • [Bes.1] M. Besbes, Points fixes des contractions définies sur un convexe $L^0$-fermé de L¹, C. R. Acad. Sci. Paris Sér. I 311 (1990), 243-246.
  • [Bes.2] M. Besbes, Complémentation de l'ensemble des points fixes d'une contraction, preprint, 1990.
  • [B-D-D-L] M. Besbes, S. Dilworth, P. Dowling and C. Lennard, New convexity and fixed point properties in Hardy and Lebesgue-Bochner spaces, preprint.
  • [Bru] R. Bruck, Properties of fixed-point sets of nonexpansive mappings in Banach spaces, Trans. Amer. Math. Soc. 179 (1973), 251-262.
  • [Day] M. M. Day, Normed Linear Spaces, Springer, Berlin 1973.
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  • [Gar] D. J. H. Garling, Subsequence principles for vector-valued random variables, Math. Proc. Cambridge Philos. Soc. 86 (1979), 301-311.
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  • [Kak] S. Kakutani, Two fixed point theorems concerning bicompact convex sets, Proc. Imperial Acad. Tokyo 14 (1938), 242-245.
  • [K-T] M. A. Khamsi and P. Turpin, Fixed points of nonexpansive mappings in Banach lattices, Proc. Amer. Math. Soc. 105 (1) (1989), 102-110.
  • [Kom] J. Komlós, A generalization of a problem of Steinhaus, Acta Math. Acad. Sci. Hungar. 18 (1967), 217-229.
  • [Kre.1] U. Krengel, Ergodic Theorems, Walter de Gruyter, Berlin 1985.
  • [Kre.2] U. Krengel, On the global limit behaviour of Markov chains and of general nonsingular Markov processes, Z. Wahrsch. Verw. Gebiete 6 (1966), 302-316.
  • [Len] C. Lennard, A new convexity property that implies a fixed point property for L₁, Studia Math. 100 (1991), 95-108.
  • [Lim] T.-C. Lim, Asymptotic centers and nonexpansive mappings in conjugate Banach spaces, Pacific J. Math. 90 (1980), 135-143.
  • [Mar] A. Markov, Quelques théorèmes sur les ensembles abéliens, Dokl. Akad. Nauk SSSR (N.S.) 10 (1936), 311-313.
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  • [Opi] Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc. 73 (1967), 591-597.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv103i1p79bwm
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