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A geometric proof of a theorem
about non-dual renormings


Author: Libor Veselý
Journal: Proc. Amer. Math. Soc. 127 (1999), 2807-2809
MSC (1991): Primary 46B03; Secondary 46B10
DOI: https://doi.org/10.1090/S0002-9939-99-05395-2
Published electronically: May 19, 1999
MathSciNet review: 1670431
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Abstract | References | Similar Articles | Additional Information

Abstract: We give a simple geometric proof of a result by Davis and Johnson that every nonreflexive Banach space $X$ admits an equivalent norm in which $X$ is not isometric to a dual space. Moreover, our renorming keeps unchanged the original norm on a given finite-codimensional subspace and makes this subspace norm-one complemented.


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

  • [DJ] W. J. DAVIS and W. B. JOHNSON, A renorming of non-reflexive Banach spaces, Proc. Amer. Math. Soc. 37 (1973), 486-488. MR 46:9693
  • [vDS] D. van DULST and I. SINGER, On Kadec-Klee norms on Banach spaces, Sudia Math. 54 (1976), 205-211. MR 52:14937
  • [D-S] N. DUNFORD and J. T. SCHWARTZ, Linear Operators I, New York 1958. MR 22:8302
  • [Ho] R. B. HOLMES, A course in Optimization and Best Approximation, Lecture Notes in Mathematics 257, Springer-Verlag, 1972. MR 54:8381
  • [Ja] R. C. JAMES, Reflexivity and the supremum of linear functionals, Ann. Math. 66 (1957), 159-169. MR 19:755g
  • [Ko] S. V. KONYAGIN, A remark on renormings of nonreflexive spaces and the existence of a Chebyshev center, Moscow Univ. Math. Bull. 43, no. 2 (1988), 55-56. MR 89g:46033
  • [Sch] H. H. SCHAEFER, Topological Vector Spaces, Graduate Texts in Mathematics, Vol. 3, Springer-Verlag, Berlin 1971. MR 49:7722

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Additional Information

Libor Veselý
Affiliation: Dipartimento di Matematica, Università degli Studi di Milano, Via C. Saldini 50, 20133 Milano, Italy
Email: libor@vmimat.mat.unimi.it

DOI: https://doi.org/10.1090/S0002-9939-99-05395-2
Received by editor(s): September 22, 1998
Received by editor(s) in revised form: November 30, 1998
Published electronically: May 19, 1999
Communicated by: Dale Alspach
Article copyright: © Copyright 1999 American Mathematical Society

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