The unconditional basic sequence problem

@article{Gowers1992TheUB,
  title={The unconditional basic sequence problem},
  author={W. T. Gowers and B. Maurey},
  journal={Journal of the American Mathematical Society},
  year={1992},
  volume={6},
  pages={851-874}
}
We construct a Banach space that does not contain any infinite un- conditional 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 par- ticular, it is either strictly singular or Fredholm with index zero. This implies that the space is not… Expand
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