It is shown that a Banach space is superreflexive if it has local unconditional structure and uniformly normal structure (UNS). A coefficient D related to UNS is introduced: D(X) is sup{lim sup n d(xn+1, con(xi: i n))}, where the sup is over all sequences {xn} with diameter 1. If X is nearly uniformly convex (NUC), then D(X) < 1. However, D(X) < 1 does not imply X is superreflexive and does not imply X is NUC even if X has UNS.
Normal type structures and superreflexivity.
CASINI, EMANUELE GIUSEPPE;
1985-01-01
Abstract
It is shown that a Banach space is superreflexive if it has local unconditional structure and uniformly normal structure (UNS). A coefficient D related to UNS is introduced: D(X) is sup{lim sup n d(xn+1, con(xi: i n))}, where the sup is over all sequences {xn} with diameter 1. If X is nearly uniformly convex (NUC), then D(X) < 1. However, D(X) < 1 does not imply X is superreflexive and does not imply X is NUC even if X has UNS.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
