Geodesic
Envelope functions and asymptotic structures in Banach spaces
Bünyamin Sarı1
1 Department of Mathematical and Statistical Sciences University of Alberta Edmonton, AB, T6G 2G1 Canada
Studia Mathematica, Tome 164 (2004) no. 3, pp. 283-306

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We introduce a notion of disjoint envelope functions to study asymptotic structures of Banach spaces. The main result gives a new characterization of asymptotic-$\ell _p$ spaces in terms of the $\ell _p$-behavior of “disjoint-permissible” vectors of constant coefficients. Applying this result to Tirilman spaces we obtain a negative solution to a conjecture of Casazza and Shura. Further investigation of the disjoint envelopes leads to a finite-representability result in the spirit of the Maurey–Pisier theorem.
DOI : 10.4064/sm164-3-6
Keywords: introduce notion disjoint envelope functions study asymptotic structures banach spaces main result gives characterization asymptotic ell spaces terms ell p behavior disjoint permissible vectors constant coefficients applying result tirilman spaces obtain negative solution conjecture casazza shura further investigation disjoint envelopes leads finite representability result spirit maurey pisier theorem

Bünyamin Sarı 1

1 Department of Mathematical and Statistical Sciences University of Alberta Edmonton, AB, T6G 2G1 Canada 
@article{10_4064_sm164_3_6,
     author = {B\"unyamin Sar{\i}},
     title = {Envelope functions and asymptotic structures
 in {Banach} spaces},
     journal = {Studia Mathematica},
     pages = {283--306},
     publisher = {mathdoc},
     volume = {164},
     number = {3},
     year = {2004},
     doi = {10.4064/sm164-3-6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/sm164-3-6/}
}
TY  - JOUR
AU  - Bünyamin Sarı
TI  - Envelope functions and asymptotic structures
 in Banach spaces
JO  - Studia Mathematica
PY  - 2004
SP  - 283
EP  - 306
VL  - 164
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4064/sm164-3-6/
DO  - 10.4064/sm164-3-6
LA  - en
ID  - 10_4064_sm164_3_6
ER  - 
%0 Journal Article
%A Bünyamin Sarı
%T Envelope functions and asymptotic structures
 in Banach spaces
%J Studia Mathematica
%D 2004
%P 283-306
%V 164
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4064/sm164-3-6/
%R 10.4064/sm164-3-6
%G en
%F 10_4064_sm164_3_6
Bünyamin Sarı. Envelope functions and asymptotic structures
 in Banach spaces. Studia Mathematica, Tome 164 (2004) no. 3, pp. 283-306. doi: 10.4064/sm164-3-6

Cité par Sources :