Geodesic
On bounded Dual-valued derivations on certain Banach algebras
Publications de l'Institut Mathématique, _N_S_86 (2009) no. 100, p. 107

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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.
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 
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     author = {A. L. Barrenechea and C. C. Pe\~na},
     title = {On bounded {Dual-valued} derivations on certain {Banach} algebras},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {107 },
     publisher = {mathdoc},
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     year = {2009},
     doi = {10.2298/PIM0900107B},
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A. L. Barrenechea; C. C. Peña. On bounded Dual-valued derivations on certain Banach algebras. Publications de l'Institut Mathématique, _N_S_86 (2009) no. 100, p. 107 . doi: 10.2298/PIM0900107B

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