Geodesic
Note on distortion and Bourgain $\ell _1$-index
Anna Maria Pelczar 1
1 Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland
Studia Mathematica, Tome 190 (2009) no. 2, pp. 147-161 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

Relations between different notions measuring proximity to $\ell _1$ and distortability of a Banach space are studied. The main result states that a Banach space all of whose subspaces have Bourgain $\ell _1$-index greater than $\omega ^\alpha $, $\alpha \omega _1$, contains either an arbitrarily distortable subspace or an $\ell _1^\alpha $-asymptotic subspace.
DOI : 10.4064/sm190-2-4
Keywords: relations between different notions measuring proximity ell distortability banach space studied main result states banach space whose subspaces have bourgain ell index greater omega alpha alpha omega contains either arbitrarily distortable subspace ell alpha asymptotic subspace

Anna Maria Pelczar  1

1 Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland 
@article{10_4064_sm190_2_4,
     author = {Anna Maria Pelczar},
     title = {Note on distortion and {Bourgain} $\ell _1$-index},
     journal = {Studia Mathematica},
     pages = {147--161},
     year = {2009},
     volume = {190},
     number = {2},
     doi = {10.4064/sm190-2-4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm190-2-4/}
}
TY  - JOUR
AU  - Anna Maria Pelczar
TI  - Note on distortion and Bourgain $\ell _1$-index
JO  - Studia Mathematica
PY  - 2009
SP  - 147
EP  - 161
VL  - 190
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm190-2-4/
DO  - 10.4064/sm190-2-4
LA  - en
ID  - 10_4064_sm190_2_4
ER  - 
%0 Journal Article
%A Anna Maria Pelczar
%T Note on distortion and Bourgain $\ell _1$-index
%J Studia Mathematica
%D 2009
%P 147-161
%V 190
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4064/sm190-2-4/
%R 10.4064/sm190-2-4
%G en
%F 10_4064_sm190_2_4
Anna Maria Pelczar. Note on distortion and Bourgain $\ell _1$-index. Studia Mathematica, Tome 190 (2009) no. 2, pp. 147-161. doi: 10.4064/sm190-2-4

Cité par Sources :