On almost isometric ideals in Banach spaces

Article Type

Research Article

Publication Title

Monatshefte fur Mathematik

Abstract

In this note we study the notion of almost isometric ideals recently introduced in Abrahamsen et al. (Glasg Math J 56:395–407, 2014) for separable Banach spaces. We show that a closed subspace of the Gurariy space that is an almost isometric ideal is itself the Gurariy space. In this space we show that all infinite dimensional M-ideals are almost isometric ideals. In c0we show that any finite codimensional proximinal ideal is an almost isometric ideal. We solve in the negative the 3-space problem for almost isometric ideals. We also give an example to show that being an almost isomeric ideal is not preserved by spaces of vector-valued continuous functions on a compact set. We show that any separable L1-predual space with a non-separable dual, has an ideal that is not an almost isometric ideal. We also study properties of almost isometric ideals that are hyperplanes.

First Page

169

Last Page

176

DOI

10.1007/s00605-015-0792-x

Publication Date

9-1-2016

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