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Operators in tight by support Banach spaces

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.

preprint2015arXivOpen access
Antonis ManoussakisAnna Pelczar-Barwacz
math.FA
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Antonis ManoussakisAnna Pelczar-Barwacz

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