Complemented subspaces of spaces obtained by interpolation
Functional Analysis
2008-02-03 v2
Abstract
If Z is a quotient of a subspace of a separable Banach space X, and V is any separable Banach space, then there is a Banach couple (A_0,A_1) such that A_0 and A_1 are isometric to , and any intermediate space obtained using the real or complex interpolation method contains a complemented subspace isomorphic to Z. Thus many properties of Banach spaces, including having non-trivial cotype, having the Radon-Nikodym property, and having the analytic unconditional martingale difference sequence property, do not pass to intermediate spaces.
Cite
@article{arxiv.math/9201212,
title = {Complemented subspaces of spaces obtained by interpolation},
author = {D. J. H. Garling and Stephen J. Montgomery-Smith},
journal= {arXiv preprint arXiv:math/9201212},
year = {2008}
}