Asymptotic symmetry in Banach spaces.
by
Simon Cowell
University of Missouri - Columbia
Coauthors: Nigel Kalton

N. Kalton introduced property (M^*) in the characterization of Banach spaces X for which K(X) is an M-ideal in L(X). A. Lima introduced property (wM^*) as a weakening of property (M^*). We show that for all e > 0, a real Banach space with property (wM^*) can be embedded isometrically in a Banach space with a shrinking (1 + e)-unconditional finite dimensional decomposition, or (1 + e)-UFDD. Moreover, this UFDD is "asymptotically 1". Similar problems were considered by A. Lima, in the presence of the UMAP.

Date received: February 29, 2008