This is an announcement for the paper "Operators in tight by support Banach spaces" by Antonis Manoussakis and Anna Pelczar-Barwacz.

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.

Archive classification: math.FA

Mathematics Subject Classification: 46B20, 46B15

Remarks: 13 pages

Submitted from: anna.pelczar@im.uj.edu.pl

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1504.02701

or

http://arXiv.org/abs/1504.02701