This is an announcement for the paper "An improvement of a theorem of Heinrich, Mankiewicz, Sims, and Yost" by Trond A. Abrahamsen.

Abstract: Heinrich, Mankiewicz, Sims, and Yost proved that every separable subspace of a Banach space Y is contained in a separable ideal in Y. We improve this result by replacing the term "ideal" with the term "almost isometric ideal". As a consequence of this we obtain, in terms of subspaces, characterizations of diameter 2 properties, the Daugavet property along with the properties of being an almost square space and an octahedral space.

Archive classification: math.FA

Mathematics Subject Classification: 46B20 (Primary) 46B07 (Secondary)

Remarks: 13 pages

Submitted from: trond.a.abrahamsen@uia.no

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1411.0425

or

http://arXiv.org/abs/1411.0425