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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The unconditional basic sequence problem
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by W. T. Gowers and B. Maurey PDF
J. Amer. Math. Soc. 6 (1993), 851-874 Request permission


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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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 6 (1993), 851-874
  • MSC: Primary 46Bxx
  • DOI:
  • MathSciNet review: 1201238