A nonlinear map for midpoint locally uniformly rotund renorming

We provide a criterion for midpoint locally uniformly rotund renormability of normed spaces involving the class of σ-slicely continuous maps, recently introduced by Moltó, Orihuela, Troyanski and Valdiva in 2003. As a consequence of this result, we obtain a theorem of G. Alexandrov concerning the th...

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Bibliographic Details
Published in:Bulletin of the Australian Mathematical Society 2005-08, Vol.72 (1), p.39-44
Main Authors: Lajara, S., Pallars, A.J.
Format: Article
Language:English
Subjects:
Banach spaces
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Summary:We provide a criterion for midpoint locally uniformly rotund renormability of normed spaces involving the class of σ-slicely continuous maps, recently introduced by Moltó, Orihuela, Troyanski and Valdiva in 2003. As a consequence of this result, we obtain a theorem of G. Alexandrov concerning the three space problem for midpoint locally uniformly rotund renormings of Banach spaces.
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972700034857