Jordan, Jordan Right and Jordan Left Derivations on Convolution Algebras

被引：0
作者：
Mohammad Hossein Ahmadi Gandomani
Mohammad Javad Mehdipour
机构：
[1] Shiraz University of Technology,Department of Mathematics
来源：
Bulletin of the Iranian Mathematical Society | 2019年 / 45卷
关键词：
Locally compact group; Jordan derivation; Jordan right derivation; Jordan left derivation; -centralizing mapping; Primary 43A15; Secondary 47B47; 16W25;
D O I：
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摘要：
In this paper, we investigate Jordan derivations, Jordan right derivations and Jordan left derivations of L0∞(G)∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_0^\infty ({{\mathcal {G}}})^*$$\end{document}. We show that any Jordan (right) derivation on L0∞(G)∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_0^\infty ({{\mathcal {G}}})^*$$\end{document} is a (right) derivation on L0∞(G)∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_0^\infty ({{\mathcal {G}}})^*$$\end{document} and the zero map is the only Jordan left derivation on L0∞(G)∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_0^\infty ({{\mathcal {G}}})^*$$\end{document}. Then, we prove that the range of a Jordan (right) derivation on L0∞(G)∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_0^\infty ({{\mathcal {G}}})^*$$\end{document} is contained into rad(L0∞(G)∗)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {rad}(L_0^\infty ({{\mathcal {G}}})^*)$$\end{document}. Finally, we establish that the product of two Jordan (right) derivations of L0∞(G)∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_0^\infty ({{\mathcal {G}}})^*$$\end{document} is always a derivation on L0∞(G)∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_0^\infty ({{\mathcal {G}}})^*$$\end{document} and there is no nonzero centralizing Jordan (right) derivation on L0∞(G)∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_0^\infty ({{\mathcal {G}}})^*$$\end{document}.
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页码：189 / 204
页数：15
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