Operators in tight by support Banach spaces
Functional Analysis
2016-02-15 v2
Abstract
We answer the question of W.T. Gowers, giving an example of a bounded operator on a subspace of Gowers unconditional space which is not a strictly singular perturbation of a restriction of a diagonal operator. We make some observations on operators in arbitrary tight by support Banach space, showing in particular that in such space no two isomorphic infinitely dimensional subspaces form a direct sum.
Cite
@article{arxiv.1504.02701,
title = {Operators in tight by support Banach spaces},
author = {Antonis Manoussakis and Anna Pelczar-Barwacz},
journal= {arXiv preprint arXiv:1504.02701},
year = {2016}
}
Comments
17 pages. Revised version - added Remark 1.2, Theorem 2.10 and corresponding changes in the paper