Geodesic
SUPERREFLEXIVITY AND $J$-CONVEXITY OF BANACH SPACES
Acta mathematica Universitatis Comenianae, Tome 66 (1997) no. 1 
J. Wenzel. SUPERREFLEXIVITY AND $J$-CONVEXITY OF BANACH SPACES. Acta mathematica Universitatis Comenianae, Tome 66 (1997) no. 1. http://geodesic.mathdoc.fr/item/AMUC_1997_66_1_a6/
@article{AMUC_1997_66_1_a6,
     author = {J. Wenzel},
     title = {SUPERREFLEXIVITY {AND} $J${-CONVEXITY} {OF} {BANACH} {SPACES}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1997},
     volume = {66},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1997_66_1_a6/}
}
TY  - JOUR
AU  - J. Wenzel
TI  - SUPERREFLEXIVITY AND $J$-CONVEXITY OF BANACH SPACES
JO  - Acta mathematica Universitatis Comenianae
PY  - 1997
VL  - 66
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AMUC_1997_66_1_a6/
ID  - AMUC_1997_66_1_a6
ER  - 
%0 Journal Article
%A J. Wenzel
%T SUPERREFLEXIVITY AND $J$-CONVEXITY OF BANACH SPACES
%J Acta mathematica Universitatis Comenianae
%D 1997
%V 66
%N 1
%U http://geodesic.mathdoc.fr/item/AMUC_1997_66_1_a6/
%F AMUC_1997_66_1_a6

Voir la notice de l'article provenant de la source Comenius University

A Banach space $X$ is superreflexive if each Banach space $Y$ that is finitely representable in $X$ is reflexive. Superreflexivity is known to be equivalent to $J$-convexity and to the non-existence of uniformly bounded factorizations of the summation operators $S_n$ through $X$. We give a quantitative formulation of this equivalence. This can in particular be used to find a factorization of $S_n$ through $X$, given a factorization of $S_N$ through $[L_2,X]$, where $N$ is `large' compared to $n$.