Weakly compact multipliers on Banach algebras related to a locally compact group

被引：0
作者：
M. J. Mehdipour
R. Nasr-Isfahani
机构：
[1] Shiraz University of Technology,Department of Mathematics
[2] Isfahan University of Technology,Department of Mathematical Sciences
来源：
Acta Mathematica Hungarica | 2010年 / 127卷
关键词：
locally compact group; multiplier; weakly compact operator; weakly completely continuous element; 43A15; 43A20; 47B07; 47B48;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study weakly compact left and right multipliers on the Banach algebra L0∞(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{G} $$\end{document})* of a locally compact group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{G} $$\end{document}. We prove that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{G} $$\end{document} is compact if and only if L0∞(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{G} $$\end{document})* has either a non-zero weakly compact left multiplier or a certain weakly compact right multiplier on L0∞(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{G} $$\end{document})*. We also give a description of weakly compact multipliers on L0∞(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{G} $$\end{document})* in terms of weakly completely continuous elements of L0t8(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{G} $$\end{document})*. Finally we show that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{G} $$\end{document} is finite if and only if there exists a multiplicative linear functional n on L0∞(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{G} $$\end{document}) such that n is a weakly completely continuous element of L0∞(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{G} $$\end{document})*
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页码：195 / 206
页数：11
相关论文
共 20 条
[1]  
Akemann C. A.(1967)Some mapping properties of the group algebras of a compact group Pacific J. Math. 22 1-8
[2]  
Ghahramani F.(1990)Isometric isomorphisms between Banach algebras related to locally compact groups Trans. Amer. Math. Soc. 321 273-283
[3]  
Lau A. T.(1992)Isomorphisms and multipliers on second dual algebras of Banach algebras Math. Proc. Cambridge Philos. Soc. 111 161-168
[4]  
Losert V.(1995)Multipliers and ideal in second conjugate algebras related to locally compact groups J. Funct. Anal. 132 170-191
[5]  
Ghahramani F.(1997)Multipliers and modulus on Banach algebras related to locally compact groups J. Funct. Anal. 150 478-497
[6]  
Lau A. T.(1987)The second dual of the group algebra of a compact group J. London Math. Soc. 35 135-148
[7]  
Ghahramani F.(1990)Concerning the second dual of the group algebra of a locally compact group J. London Math. Soc. 41 445-460
[8]  
Lau A. T.(2004)Weakly compact multipliers on group algebras J. Funct. Anal. 213 466-472
[9]  
Ghahramani F.(2007)Completely continuous elements of Banach algebras related to locally compact groups Bull. Austral. Math. Soc. 76 49-54
[10]  
Lau A. T.(2003)Compact elements of the algebras PM Acta Math. Hungar. 101 83-92
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