On the Existence of Asymptotic-lp Structures in Banach Spaces
Canadian mathematical bulletin, Tome 50 (2007) no. 4, pp. 619-631
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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\,\le \,p\,\le \,\infty $ . This extends a result by Figiel, Frankiewicz, Komorowski and Ryll-Nardzewski.
Tcaciuc, Adi. On the Existence of Asymptotic-lp Structures in Banach Spaces. Canadian mathematical bulletin, Tome 50 (2007) no. 4, pp. 619-631. doi: 10.4153/CMB-2007-061-3
@article{10_4153_CMB_2007_061_3,
author = {Tcaciuc, Adi},
title = {On the {Existence} of {Asymptotic-lp} {Structures} in {Banach} {Spaces}},
journal = {Canadian mathematical bulletin},
pages = {619--631},
year = {2007},
volume = {50},
number = {4},
doi = {10.4153/CMB-2007-061-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2007-061-3/}
}
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