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On the Existence of Asymptotic-$l_p$ Structures in Banach Spaces |
Canad. Math. Bull. 50(2007), 619-631
Published:2007-12-01
Printed: Dec 2007
Printed: Dec 2007
- Adi Tcaciuc
Abstract
It is shown that if a Banach space is saturated with infinite
dimensional subspaces in which all ``special" $n$-tuples of
vectors are equivalent with constants independent of $n$-tuples and
of $n$, then the space contains asymptotic-$l_p$ subspaces
for some $1 \leq p \leq \infty$.
This extends a result by Figiel, Frankiewicz, Komorowski and
Ryll-Nardzewski.
| MSC Classifications: |
46B20 - Geometry and structure of normed linear spaces 46B40 - Ordered normed spaces [See also 46A40, 46B42] 46B03 - Isomorphic theory (including renorming) of Banach spaces |