The unconditional basic sequence problem

Authors:
W. T. Gowers and B. Maurey

Journal:
J. Amer. Math. Soc. **6** (1993), 851-874

MSC:
Primary 46Bxx

MathSciNet review:
1201238

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Abstract: We construct a Banach space that does not contain any infinite unconditional basic sequence and investigate further properties of this space. For example, it has no subspace that can be written as a topological direct sum of two infinite-dimensional spaces. This property implies that every operator on the space is a strictly singular perturbation of a multiple of the identity. In particular, it is either strictly singular or Fredholm with index zero. This implies that the space is not isomorphic to any proper subspace.

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DOI:
https://doi.org/10.1090/S0894-0347-1993-1201238-0

Article copyright:
© Copyright 1993
American Mathematical Society