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. 
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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