Geodesic
Uniform non-\(\ell_1^n\)-ness of \(\ell_1\)-sums of Banach spaces
Commentationes Mathematicae, Tome 47 (2007) no. 2, pp. 161-169.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

We shall characterize the uniform non-\(\ell_1^n\)-ness of the \(\ell_1\)-sum \((X_1 \oplus\dots\oplus X_m)_1\) of a finite number of Banach spaces \(X_1 ,\dots, X_m\). Also we shall obtain that \((X_1 \oplus \dots \oplus X_m)_1\) is uniformly non-\(\ell_1^{m+1}\) if and only if all \(X_1 ,\dots , X_m\) are uniformly non-square (note that \((X_1 \oplus \dots \oplus X_m)_1\) is not uniformly non-\(\ell_1^m\)). Several related results will be presented.
DOI : 10.14708/cm.v47i2.5246
Mots-clés : \(\ell_1\)-sum of Banach spaces, uniformly non-square space, uniformly non-\(\ell_1^n\)-space, super-reflexivity, fixed point property 
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Mikio Kato; Takayuki Tamura. Uniform non-\(\ell_1^n\)-ness of \(\ell_1\)-sums of Banach spaces. Commentationes Mathematicae, Tome 47 (2007) no. 2, pp.  161-169. doi : 10.14708/cm.v47i2.5246. http://geodesic.mathdoc.fr/articles/10.14708/cm.v47i2.5246/

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