## The unconditional basic sequence problem

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- by W. T. Gowers and B. Maurey
- J. Amer. Math. Soc.
**6**(1993), 851-874 - DOI: https://doi.org/10.1090/S0894-0347-1993-1201238-0
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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.## References

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## Bibliographic Information

- © Copyright 1993 American Mathematical Society
- Journal: J. Amer. Math. Soc.
**6**(1993), 851-874 - MSC: Primary 46Bxx
- DOI: https://doi.org/10.1090/S0894-0347-1993-1201238-0
- MathSciNet review: 1201238