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A renorming of nonreflexive Banach spaces

Authors: William J. Davis and William B. Johnson
Journal: Proc. Amer. Math. Soc. 37 (1973), 486-488
MSC: Primary 46B05
MathSciNet review: 0310595
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Abstract: Every nonreflexive Banach space can be equivalently renormed in such a way that it is not isometrically a conjugate space.

References [Enhancements On Off] (What's this?)

  • [1] J. Dixmier, Sur un théorème de Banach, Duke Math. J. 15 (1948), 1057–1071 (French). MR 0027440
  • [2] M. Ĭ. Kadec′, On the connection between weak and strong convergence, Dopovidi Akad. Nauk Ukraïn. RSR 1959 (1959), 949–952 (Ukrainian, with Russian and English summaries). MR 0112021
  • [3] M. Ĭ. Kadec′, Topological equivalence of all separable Banach spaces, Dokl. Akad. Nauk SSSR 167 (1966), 23–25 (Russian). MR 0201951
  • [4] M. Ĭ. Kadec′ and A. Pelčin′ski, Basic sequences, bi-orthogonal systems and norming sets in Banach and Fréchet spaces, Studia Math. 25 (1965), 297–323 (Russian). MR 0181886
  • [5] V. L. Klee Jr., Some characterizations of reflexivity, Revista Ci., Lima 52 (1950), no. nos. 3-4, 15–23. MR 0043364
  • [6] V. Klee, Mappings into normed linear spaces, Fund. Math. 49 (1960/1961), 25–34. MR 0126690
  • [7] J. Rainwater, On a renorming theorem of Klee (preprint).
  • [8] Ivan Singer, Bases in Banach spaces. I, Springer-Verlag, New York-Berlin, 1970. Die Grundlehren der mathematischen Wissenschaften, Band 154. MR 0298399

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Keywords: Nonreflexive space, conjugate space, dual space
Article copyright: © Copyright 1973 American Mathematical Society