A geometric proof of a theorem about non-dual renormings

Veselý, Libor

doi:10.1090/S0002-9939-99-05395-2

A geometric proof of a theorem about non-dual renormings
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Proc. Amer. Math. Soc. 127 (1999), 2807-2809 Request permission

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.

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