Proceedings of the American Mathematical Society

Author(s): Libor Veselý
Journal: Proc. Amer. Math. Soc. 127 (1999), 2807-2809.
MSC (1991): Primary 46B03; Secondary 46B10
Posted: May 19, 1999
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Abstract: We give a simple geometric proof of a result by Davis and Johnson that every nonreflexive Banach space

admits an equivalent norm in which

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.

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[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
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[Sch]: H. H. SCHAEFER, Topological Vector Spaces, Graduate Texts in Mathematics, Vol. 3, Springer-Verlag, Berlin 1971. MR 49:7722

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