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Some results on second transpose of a dual valued derivation | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 52، دوره 10، شماره 2، اسفند 2019، صفحه 267-273 اصل مقاله (314.87 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2019.4195 | ||
| نویسنده | ||
| Morteza Essmaili* | ||
| Department of Mathematics, Faculty of Mathematical and Computer Science, Kharazmi University, 50 Taleghani Avenue, 15618 Tehran, Iran | ||
| تاریخ دریافت: 14 خرداد 1397، تاریخ بازنگری: 27 مرداد 1397، تاریخ پذیرش: 20 شهریور 1397 | ||
| چکیده | ||
| Let $A$ be a Banach algebra and $X$ be an arbitrary Banach $A$-module. In this paper, we study the second transpose of derivations with value in dual Banach $A$-module $X^{*}.$ Indeed, for a continuous derivation $D:A\longrightarrow X^{*}$ we obtain a necessary and sufficient condition such that the bounded linear map $\Lambda\circ D^{\prime\prime}:A^{**}\longrightarrow X^{***}$ to be a derivation, where $\Lambda$ is composition of restriction and canonical injection maps. This characterization generalizes some well known results in [2]. | ||
| کلیدواژهها | ||
| Derivation؛ second transpose؛ Banach module؛ module actions | ||
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