Almost isometric ideals in Banach spaces
Functional Analysis
2013-06-21 v2
Abstract
A natural class of ideals, almost isometric ideals, of Banach spaces is defined and studied. The motivation for working with this class of subspaces is our observation that they inherit diameter 2 properties and the Daugavet property. Lindenstrauss spaces are known to be the class of Banach spaces that are ideals in every superspace; we show that being an almost isometric ideal in every superspace characterizes the class of Gurariy spaces.
Keywords
Cite
@article{arxiv.1206.3539,
title = {Almost isometric ideals in Banach spaces},
author = {Trond A. Abrahamsen and Vegard Lima and Olav Nygaard},
journal= {arXiv preprint arXiv:1206.3539},
year = {2013}
}
Comments
13 pages. Original title "Super-ideals in Banach spaces"