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# On the Existence of Asymptotic-$l_p$ Structures in Banach Spaces

Published:2007-12-01
Printed: Dec 2007
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.