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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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: http://dx.doi.org/10.1090/S0894-0347-1993-1201238-0
PII: S 0894-0347(1993)1201238-0
Article copyright: © Copyright 1993 American Mathematical Society