Operators in tight by support Banach spacesOperators in tight by support Banach spaces Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2018-10-162016enAnswering the question of W. T. Gowers, we give 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 a space no two isomorphic infinitely dimensional subspaces form a direct sum.http://creativecommons.org/licenses/by/4.0/Journal of the London Mathematical Society932464-480 Manousakis Antonios Μανουσακης Αντωνιος Pelczar-Barwacz Anna Oxford University Press Banach spaces