On the continuity of some linear maps on certain Banach algebras
الموضوعات :
1 - Department of Mathematics, University of Kurdistan, Sanandaj, Iran
2 - Department of Mathematics, University of Kurdistan, Sanandaj, Iran
الکلمات المفتاحية: derivation, Multiplier, Automatic continuity, Lau product,
ملخص المقالة :
Let $\mathcal{A}$ and $\mathcal{U}$ be Banach algebras, $\theta$ be a nonzero character on $\mathcal{A}$ and let ${\mathcal{A}}\times_{\theta}{\mathcal{U}}$ be the corresponding Lau product Banach algebra. In this paper we investigate derivations and multipliers of ${\mathcal{A}}\times_{\theta}{\mathcal{U}}$ and study the automatic continuity of these maps. We also study continuity of the derivations for some special cases of $\mathcal{U}$ and the Banach $({{\mathcal{A}}\times_{\theta}\mathcal{U}})$-bimodule ${\mathcal{X}}$ and establish various results in this respect. Some of the results are devoted to find conditions under which one can represent a derivation on ${{\mathcal{A}}\times_{\theta}\mathcal{U}}$ as sum of two derivations in such a way that one of them is continuous. Some examples are also given.
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