Geodesic
A new geometrical constant of Banach spaces and the uniform normal structure
Commentationes Mathematicae, Tome 49 (2009) no. 1, pp. 3-13.

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

We introduce and study a new geometrical constant \(\gamma_{X,\psi\) of a Banach space \(X\), by using the notion of \(\psi\)-direct sum given in [Y. Takahashi, M. Kato and K.-S. Saito, J. Inequal. Appl. 7 (2002), 179-186]. At first, we characterize uniform non-squareness in terms of \(\gamma_{X,\psi}\). Moreover, we consider Banach spaces having uniform normal structure.
DOI : 10.14708/cm.v49i1.5274
Mots-clés : absolute norm, \(\psi\)-direct sum, uniformly non-square, uniform normal structure 
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Ken-Ichi Mitani; Kichi-Suke Saito. A new geometrical constant of Banach spaces and the uniform normal structure. Commentationes Mathematicae, Tome 49 (2009) no. 1, pp.  3-13. doi : 10.14708/cm.v49i1.5274. http://geodesic.mathdoc.fr/articles/10.14708/cm.v49i1.5274/

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