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    Gulevich, N. M. 1996. Fixed points of nonexpansive mappings. Journal of Mathematical Sciences, Vol. 79, Issue. 1, p. 755.
    Sims, Brailey and Smyth, M. 1995. ON NON-UNIFORM CONDITIONS GIVING WEAK NORMAL STRUCTURE. Quaestiones Mathematicae, Vol. 18, Issue. 1-3, p. 9.
    Yu, Xin Tai 1988. A geometrically aberrant Banach space with uniformly normal structure. Bulletin of the Australian Mathematical Society, Vol. 38, Issue. 01, p. 99.
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A geometrically aberrant Banach space with normal structure

  • J.R. Giles (a1), Brailey Sims (a2) and S. Swaminathan (a3)
Abstract

An example is given of a Banach space with normal structure which does not satisfy the geometrical conditions commonly expected to be related to normal structure.

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COPYRIGHT: © Australian Mathematical Society 1985
References
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[1]Javier, Bernal and Francis, Sullivan, “Banach spaces that have normal structure and are isomorphic to a Hilbert space”, Proc. Amer. math. Soc. 90 (1984), 550–554.
[2]Brodskii, M.S. and Milman, D.P., “On the centre of a convex set”, Dokl. Akad. Nauk SSSR 59 (1948), 837–840.
[3]Brown, A.L., “A rotund reflexive space having a subspace of codimension two with a discontinuous metric projection”, Michigan Math. J. 21 (1974), 145–151.
[4]Day, M.M., James, R.C. and Swaminathan, S., “Normed linear spaces that are uniformly convex in every direction”, Canad. J. Math. 23 (1971), 1051–1059.
[5]Edelstein, M., “A theorem on fixed points under isometries”, Amer. Math. Monthly 70 (1963), 298–300.
[6]Fan, Ky and Glicksberg, Irving, “Some geometric properties of the spheres in a normed linear space”, Duke Math. J. 25 (1958), 553–568.
[7]Giles, J.R., “Uniformly weak differentiability of the norm and a condition of Vlasov”, J. Austral. Math. Soc. Ser. A 21 (1976), 393–409.
[8]Gillespie, A.A. and Williams, B.B., “Fixed point theorem for non-expansive mappings on Banach spaces with uniformly normal structure”, Applicable Anal. 9 (1979), 121–214.
[9]Maluta, E., “Uniformly normal structure and related coefficients”, Pacific J. Math. (to appear).
[10]Smith, Mark A. and Turett, Barry, “A reflexive LUR Banach space that lacks normal structure”, preprint.
[11]Swaminathan, S., “Normal structure in Banach spaces and its generalisations”, Contemp. Math. 18 (1983), 101–215.
[12]Dulst, D. Van and Sims, Brailey, “Fixed points of non-expansive mappings and Chebychev centres in Banach spaces with norms of type (KK)”, Banach space theory and its applications, Bucharest 1981, 91–95 (Lecture Notes in Mathematics, 991. Springer-verlag, Berlin, Heidelberg, New York, 1983).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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