Universal spaces for strictly convex Banach Spaces.
Gilles Godefroy (2006)
RACSAM
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We show that if a separable Banach space X contains an isometric copy of every strictly convex separable Banach space, then X contains an isometric copy of l equipped with its natural norm. In particular, the class of strictly convex separable Banach spaces has no universal element. This provides a negative answer to a question asked by J. Lindenstrauss.