Stability of weak normal structure in James quasi reflexive space

Abstract

We introduce a coefficient on general Banach spaces which allows us to derive the weak normal structure for those Banach spaces whose Banach-Mazur distance to James quasi reflexive space is less than

Normal structure and fixed point property

“…They introduce the semi-Opial property, mainly with the technical role of guaranteeing the FPP for a space Ri®A"2 provided that the space X 2 has FPP. Thus, if the space A'j is uniformly convex in every direction UCED and the second space X 2 verifies the semi-Opial property, then the /,-product X A ®, X 2 have the FPP.Here we also show that if the space A^ has the generalized Gossez-Lami Dozo property (a known sufficient condition for weak normal structure [8]) and the second space X 2 verifies the semi-Opial property, then the /,-product X 1 <8> i X 2 has the FPP. The scope of this last result is different from that of Theorem (1) of [11].…”

“…Here we also show that if the space A^ has the generalized Gossez-Lami Dozo property (a known sufficient condition for weak normal structure [8]) and the second space X 2 verifies the semi-Opial property, then the /,-product X 1 <8> i X 2 has the FPP. The scope of this last result is different from that of Theorem (1) of [11].…”

Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings

“…Since X has the fixed point property for nonexpansive mappings (see [7]), there exists an f -ergodic retraction R from C onto F ix(f ). We shall prove that F ix(f ) = F ix(T ).…”

On some Banach space properties sufficient for weak normal structure and their permanence properties

“…With D[(x n )] := lim sup n lim sup m x n − x m for a bounded sequence (x n ), [12] defines β(X) := inf{D[(x n )] : x n → 1, x n w − → 0}.…”

“…In [12] a Banach space was said to satisfy the Generalized Gossez-Lami Dozo property (GGLD) if the original inequality defining WO holds with sup m replaced by lim sup m . The following was proved in [19].…”