On bounded Dual-valued derivations on certain Banach algebras

A. L. Barrenechea ; C. C. Peña

Publications de l'Institut Mathématique, _N_S_86 (2009) no. 100, p. 107

Résumé

We consider the class $\mathfrak{D}(\mathcal{U})$of bounded derivations $\mathcal{U}\overset{d}\to\mathcal{U}^*$defined on a Banach algebra $\mathcal{U}$ with values in its dual space $\mathcal{U}^*$so that $\langle x,d(x)\rangle =0$ for all $x\in \mathcal{U}$.The existence of such derivations is shown, but lacking the simplest structure of an inner one.We characterize the elements of $\mathfrak{D}(\mathcal{U})$if $\operatorname{span}(\mathcal{U}^2)$ is dense in $\mathcal{U}$or if $\mathcal{U}$ is a unitary dual Banach algebra.

Détail

DOI : 10.2298/PIM0900107B

Classification : 46H35 47D30
Keywords: Dual Banach algebras, approximation property, dual Banach pairs, nuclear operators, shrinking basis and associated sequence of coefficient functionals