Sufficient conditions for normal structure of a Banach space are given. One of them implies reflexivity for Banach spaces with an unconditional basis, and also for Banach lattices.
Departamento de Análisis Matemático, Facultad de Matemáticas, Dr. Moliner 50, 46100 Burjassot, Valencia, Spain
Bibliografia
[B] J. Banaś, On modulus of noncompact convexity and its properties, Canad. Math. Bull. 30 (1987), 186-192.
[D-S] D. van Dulst and B. Sims, Fixed points of nonexpansive mappings and Chebyshev centers in Banach spaces with norms of type (KK), in: Banach Space Theory and Its Applications, Lecture Notes in Math. 991, Springer, Berlin, 1983, 35-43.
[G-J-L] J. García-Falset, A. Jiménez-Melado and E. Lloréns-Fuster, A characterization of normal structure, in: Proc. Second Internat. Conf. Fixed Point Theory and Appl., Halifax, 1991, K. K. Tan (ed.), World Sci., Singapore, 1992, 122-129.
[G-K] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Stud. Adv. Math. 28, Cambridge Univ. Press, 1990.
[G-S] K. Goebel and T. Sękowski, The modulus of noncompact convexity, Ann. Univ. Mariae Curie-Skłodowska 38 (1984), 41-48.
[G-LD] J. P. Gossez and E. Lami Dozo, Some geometrical properties related to the fixed-point theory for nonexpansive mappings, Pacific J. Math. 40 (1972), 565-573.
[H] R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 743-749.
[K] W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006,.
[KU] D. N. Kutzarova, Every (β)-space has the Banach-Saks property, C. R. Acad. Bulgare Sci. 42 (11) (1989), 9-11.
[L-Tz] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces I-II, Springer, 1977.
[L] T. Landes, Normal structure and the sum property, Pacific J. Math. 123 (1986), 127-147.
[M] V. Montesinos, Drop property equals reflexivity, Studia Math. 87 (1987), 93-100.
[N-S-W] J. L. Nelson, K. L. Singh and J. H. M. Whitfield, Normal structures and nonexpansive mappings in Banach spaces, in: Nonlinear Analysis, Th. M. Rhassias (ed.), World Sci., Singapore, 1987, 433-492.
[R1] S. Rolewicz, On drop property, Studia Math. 85 (1987), 27-35.
[R2] S. Rolewicz, On Δ-uniform convexity and drop property, ibid. 87 (1987), 181-191.
[S] B. Sims, Fixed points of nonexpansive maps on weak and weak*-compact sets, Queen's Univ. of Kingston Lecture Notes, 1982.
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Bibliografia
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