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The Herz–Schur multiplier norm of sets satisfying the Leinert condition

Tom 124 / 2011

Éric Ricard, Ana-Maria Stan Colloquium Mathematicum 124 (2011), 255-274 MSC: Primary 43A22, 46L07, 47L07. DOI: 10.4064/cm124-2-10

Streszczenie

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 $\def\F{{\mathbb F}}\|\chi_E\|_{M_{cb}A(\F)}$.

Autorzy

  • Éric RicardLaboratoire de Département de Mathématiques
    Université Franche-Comté
    25000 Besançon, France
    e-mail
  • Ana-Maria StanLaboratoire de Département de Mathématiques
    Université Franche-Comté
    Besançon, 25000, France
    e-mail

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