Address:
Department of Mathematics, Semnan University, P. O. Box 35195-363, Semnan, Iran
Department of Mathematics, Faculty of Science, Urmia University, Urmia, Iran
Department of Mathematics, Malayer University, Malayer, Hamedan, Iran
E-mail:
madjid.eshaghi@gmail.com
habibianf72@yahoo.com
ebadian.ali@gmail.com
hayati@malayeru.ac.ir
Abstract:Let $\mathcal{A}$ be a dual Banach algebra. We investigate the first weak$^*$-continuous cohomology group of $\mathcal{A}$ with coefficients in $\mathcal{A}$. Hence, we obtain conditions on ${\mathcal{A}}$ for which \[ H^1_{w^*}(\mathcal{A}, \mathcal{A})=\lbrace 0\rbrace \,. \]
AMSclassification:primary 46H25.
Keywords:Arens product, 2-weakly amenable, derivation.