Geodesic
Envelope functions and asymptotic structures in Banach spaces
Bünyamin Sarı1
1Department 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 
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
@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},
     year = {2004},
     volume = {164},
     number = {3},
     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
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
%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

Cité par Sources :