New York Journal of Mathematics
Volume 18 (2012) 657-665


María J. Aleandro and Carlos C. Peña

On dual-valued operators on Banach algebras

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Published: September 27, 2012
Keywords: Arens products, amenable and weakly amenable Banach algebras, dual Banach algebras, Beurling algebras
Subject: 46H35, 47D30

Let U be a regular Banach algebra and let D:UU be a bounded linear operator, where U is the topological dual space of U. We seek conditions under which the transpose of D becomes a bounded derivation on U∗∗. We focus our attention on the class D(U) of bounded derivations D:UU so that <a,D(a)>=0 for all a∈U. We consider this matter in the setting of Beurling algebras on the additive group of integers. We show that U is a weakly amenable Banach algebra if and only if D(U)≠{0}.

Author information

María J. Aleandro:
CONICET - UNCPBA. FCExactas, Dpto. de Matemáticas, NUCOMPA.

Carlos C. Peña:
UNCPBA. FCExactas, Dpto. de Matemáticas, NUCOMPA.