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The unconditional basic sequence problem
Author(s):
W. T.
Gowers;
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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Additional Information:
DOI:
10.1090/S0894-0347-1993-1201238-0
PII:
S0894-0347-1993-1201238-0
Copyright of article:
Copyright
1993,
American Mathematical Society
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