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On Antichains of Spreading Models of Banach Spaces |
Published:2009-12-04
Printed: Mar 2010
Printed: Mar 2010
- Pandelis Dodos
Abstract
We show that for every separable Banach space $X$,
either $\mathrm{SP_w}(X)$ (the set of all spreading models
of $X$ generated by weakly-null sequences in $X$, modulo
equivalence) is countable, or $\mathrm{SP_w}(X)$ contains an
antichain of the size of the continuum. This answers
a question of S.~J. Dilworth, E. Odell, and B. Sari.
| MSC Classifications: |
46B20 - Geometry and structure of normed linear spaces 03E15 - Descriptive set theory [See also 28A05, 54H05] |