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

  Published:2007-12-01
 Printed: Dec 2007
  • Adi Tcaciuc
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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, 46B40, 46B03 show english descriptions Geometry and structure of normed linear spaces
Ordered normed spaces [See also 46A40, 46B42]
Isomorphic theory (including renorming) of Banach spaces
46B20 - Geometry and structure of normed linear spaces
46B40 - Ordered normed spaces [See also 46A40, 46B42]
46B03 - Isomorphic theory (including renorming) of Banach spaces
 

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