Geodesic
Small subspaces of $L_p$
Richard Haydon1 ; Edward Odell2 ; Thomas Schlumprecht3
1 Brasenose College<br/>Oxford OX1 4AJ <br/> U.K.
2 The University of Texas at Austin<br/> Austin, TX 78712
3 Brasenose College<br/> Oxford OX1 4AJ<br/> U.K.
Annals of mathematics, Tome 173 (2011) no. 1, pp. 169-209.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that if $X$ is a subspace of $L_p$ $(2\lt p\lt \infty)$, then either $X$ embeds isomorphically into $\ell_p \oplus \ell_2$ or $X$ contains a subspace $Y,$ which is isomorphic to $\ell_p(\ell_2)$. We also give an intrinsic characterization of when $X$ embeds into $\ell_p \oplus \ell_2$ in terms of weakly null trees in $X$ or, equivalently, in terms of the “infinite asymptotic game” played in $X$. This solves problems concerning small subspaces of $L_p$ originating in the 1970’s. The techniques used were developed over several decades, the most recent being that of weakly null trees developed in the 2000’s.
DOI : 10.4007/annals.2011.173.1.5

Richard Haydon 1 ; Edward Odell 2 ; Thomas Schlumprecht 3

1 Brasenose College<br/>Oxford OX1 4AJ <br/> U.K.
2 The University of Texas at Austin<br/> Austin, TX 78712
3 Brasenose College<br/> Oxford OX1 4AJ<br/> U.K. 
@article{10_4007_annals_2011_173_1_5,
     author = {Richard Haydon and Edward Odell and Thomas Schlumprecht},
     title = {Small subspaces of $L_p$},
     journal = {Annals of mathematics},
     pages = {169--209},
     publisher = {mathdoc},
     volume = {173},
     number = {1},
     year = {2011},
     doi = {10.4007/annals.2011.173.1.5},
     mrnumber = {2753602},
     zbl = {05960658},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.1.5/}
}
TY  - JOUR
AU  - Richard Haydon
AU  - Edward Odell
AU  - Thomas Schlumprecht
TI  - Small subspaces of $L_p$
JO  - Annals of mathematics
PY  - 2011
SP  - 169
EP  - 209
VL  - 173
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.1.5/
DO  - 10.4007/annals.2011.173.1.5
LA  - en
ID  - 10_4007_annals_2011_173_1_5
ER  - 
%0 Journal Article
%A Richard Haydon
%A Edward Odell
%A Thomas Schlumprecht
%T Small subspaces of $L_p$
%J Annals of mathematics
%D 2011
%P 169-209
%V 173
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.1.5/
%R 10.4007/annals.2011.173.1.5
%G en
%F 10_4007_annals_2011_173_1_5
Richard Haydon; Edward Odell; Thomas Schlumprecht. Small subspaces of $L_p$. Annals of mathematics, Tome 173 (2011) no. 1, pp. 169-209. doi : 10.4007/annals.2011.173.1.5. http://geodesic.mathdoc.fr/articles/10.4007/annals.2011.173.1.5/

Cité par Sources :