Unconditional structures of weakly null sequences (Q2701694)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unconditional structures of weakly null sequences |
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Unconditional structures of weakly null sequences (English)
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19 February 2001
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Ramsey theory
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weakly null sequence
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convex block basis
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convex block subsequence
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boundedly convexly complete
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The following dichotomy is established for a normalized weakly null sequence in a Banach space: Either every subsequence admits a convex block subsequence equivalent to the unit vector basis of \(c_0\), or there exists a subsequence which is boundedly convexly complete. This paper also gives a unified approach to this result with previously known results related to sequences in Banach spaces.
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