Geodesic
The unconditional basic sequence problem
Journal of the American Mathematical Society, Tome 06 (1993) no. 4, pp. 851-874

Voir la notice de l'article provenant de la source American Mathematical Society

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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Gowers, W. T.; Maurey, B. The unconditional basic sequence problem. Journal of the American Mathematical Society, Tome 06 (1993) no. 4, pp. 851-874. doi: 10.1090/S0894-0347-1993-1201238-0

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