(2n − 1)-Ideal amenability of triangular banach algebras

被引：0
作者：
S ETEMAD
M ETTEFAGH
机构：
[1] Islamic Azad University,Young Researchers and Elite Club, Tabriz Branch
[2] Islamic Azad University,Department of Mathematics, Tabriz Branch
来源：
Proceedings - Mathematical Sciences | 2015年 / 125卷
关键词：
Amenability; ideal amenability; triangular Banach algebras; Primary: 46H20; Secondary: 46H25, 16E40;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {A}$\end{document} and ℬ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {B}$\end{document} be two unital Banach algebras and let ℳ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {M}$\end{document} be an unital Banach A,ℬ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {A}, \mathcal {B}$\end{document}-module. Also, let T=Aℳℬ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {T}=\left [\begin {array}{cc} \mathcal {A} & \mathcal {M} \\ & \mathcal {B} \end {array}\right ]$\end{document} be the corresponding triangular Banach algebra. Forrest and Marcoux (Trans. Amer. Math. Soc.354 (2002) 1435–1452) have studied the n-weak amenability of triangular Banach algebras. In this paper, we investigate (2n−1)-ideal amenability of T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {T}$\end{document} for all n≥1. We introduce the structure of ideals of these Banach algebras and then, we show that (2n−1)-ideal amenability of T\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {T}$\end{document} depends on (2n−1)-ideal amenability of Banach algebras A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {A}$\end{document} and ℬ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal {B}$\end{document}.
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页码：199 / 207
页数：8
相关论文
共 15 条
  • [1] Abbaspour Gh(2010)Ideal amenability of triangular Banach algebras Int. J. Contemp. Math. Anal. 4 1285-1290
  • [2] Bade WG(1987)Amenability and weak amenability for Beurling and Lipschits algebra Proc. London Math. Soc. 55 359-377
  • [3] Curtis PG(1998)Derivations into iterated duals of Banach algebras Studia Math. 128 19-54
  • [4] Dales HG(1996)Derivations of triangular Banach algebras Indiana Univ. Math. J. 45 441-462
  • [5] Dales HG(2002)Weak amenability of triangular Banach algebras Trans. Amer. Math. Soc. 354 1435-1452
  • [6] Ghahramani F(2008)Derivations into n-th duals of ideals of Banach algebras Bull. Iranian Math. Soc. 34 59-71
  • [7] Gronbaek N(2004)Derivations into duals of ideals of Banach algebras Proc. Indian Acad. Sci. 114 399-408
  • [8] Forrest BE(undefined)undefined undefined undefined undefined-undefined
  • [9] Marcoux LW(undefined)undefined undefined undefined undefined-undefined
  • [10] Forrest BE(undefined)undefined undefined undefined undefined-undefined
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