Operators in tight by support Banach spaces
arXiv:1504.02701 · doi:10.1112/jlms/jdv072
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.
17 pages. Revised version - added Remark 1.2, Theorem 2.10 and corresponding changes in the paper