The unconditional basic sequence problem
W. T. Gowers, Bernard Maurey
TL;DR
This paper constructs a Banach space that notably lacks any infinite unconditional basic sequence, addressing a fundamental problem in the structure theory of Banach spaces.
Contribution
It introduces a new Banach space example that does not contain any infinite unconditional basic sequence, solving a longstanding open problem.
Findings
Existence of a Banach space without infinite unconditional basic sequences
Advancement in understanding the structure of Banach spaces
Provides a counterexample to previous conjectures
Abstract
We construct a Banach space that does not contain any infinite unconditional basic sequence.
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Optimization and Variational Analysis