We consider a family of renormings of the infinite-dimensional separable Hilbert space introduced in literature by R.C. James in the sixties and prove that all its members are P-convex. It is known that these spaces lack normal structure when they are sufficiently far, in the sense of the Banach-Mazur distance, from being Hilbert, hence our result provides the first example of a P-convex space without normal structure.
A class of P-convex spaces lacking normal structure
MALUTA, ELISABETTA
2012-01-01
Abstract
We consider a family of renormings of the infinite-dimensional separable Hilbert space introduced in literature by R.C. James in the sixties and prove that all its members are P-convex. It is known that these spaces lack normal structure when they are sufficiently far, in the sense of the Banach-Mazur distance, from being Hilbert, hence our result provides the first example of a P-convex space without normal structure.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
NA9364-pubbl.pdf
Accesso riservato
:
Post-Print (DRAFT o Author’s Accepted Manuscript-AAM)
Dimensione
404.06 kB
Formato
Adobe PDF
|
404.06 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.