Geodesic
The Herz–Schur multiplier norm of sets satisfying the Leinert condition
Éric Ricard1 ; Ana-Maria Stan2
1 Laboratoire de Département de Mathématiques Université Franche-Comté 25000 Besançon, France
2 Laboratoire de Département de Mathématiques Université Franche-Comté Besançon, 25000, France
Colloquium Mathematicum, Tome 124 (2011) no. 2, pp. 255-274.

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

It is well known that in a free group $\def\F{{\mathbb F}}\F$, one has $\def\F{{\mathbb F}}\|\chi_E\|_{M_{cb}A(\F)}\leq 2$, where $E$ is the set of all the generators. We show that the (completely) bounded multiplier norm of any set satisfying the Leinert condition depends only on its cardinality. Consequently, based on a result of Wysoczański, we obtain a formula for $\def\F{{\mathbb F}}\|\chi_E\|_{M_{cb}A(\F)}$.
DOI : 10.4064/cm124-2-10
Keywords: known group def mathbb has def mathbb chi leq where set generators completely bounded multiplier norm set satisfying leinert condition depends only its cardinality consequently based result wysocza ski obtain formula def mathbb chi

Éric Ricard 1 ; Ana-Maria Stan 2

1 Laboratoire de Département de Mathématiques Université Franche-Comté 25000 Besançon, France
2 Laboratoire de Département de Mathématiques Université Franche-Comté Besançon, 25000, France 
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Éric Ricard; Ana-Maria Stan. The Herz–Schur multiplier norm of  sets satisfying the Leinert condition. Colloquium Mathematicum, Tome 124 (2011) no. 2, pp. 255-274. doi : 10.4064/cm124-2-10. http://geodesic.mathdoc.fr/articles/10.4064/cm124-2-10/

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