Universal spaces for strictly convex Banach Spaces.
Godefroy, Gilles
RACSAM, Tome 100 (2006), p. 137-146 / Harvested from Biblioteca Digital de Matemáticas
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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 l1 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.

Probamos que si un espacio separable X contiene una copia isométrica de todo espacio estrictamente convexo separable, entonces X contiene una copia isométrica de l1 con su norma natural. En particular, la clase de los espacios de Banach estrictamente convexos no tiene elemento universal. Esto responde negativamente a una pregunta de J. Lindenstrauss.

Publié le : 2006-01-01
DMLE-ID : 4148 
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     title = {Universal spaces for strictly convex Banach Spaces.},
     journal = {RACSAM},
     volume = {100},
     year = {2006},
     pages = {137-146},
     mrnumber = {MR2267405},
     zbl = {1118.46019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41647}
}

Godefroy, Gilles. Universal spaces for strictly convex Banach Spaces.. RACSAM, Tome 100 (2006) pp. 137-146. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41647/