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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
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.


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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: http://dx.doi.org/10.1090/S0002-9939-99-05395-2
PII: S 0002-9939(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