Ideal Connes-Amenability of Certain Dual Banach Algebras

摘要

Abstract In this paper, we show that for every discrete weakly cancellative inverse semigroup S, the semigroup algebra l1(S)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$l^{1}(S)$$end{document} is ideally Connes-amenable. We also prove that the Lipschitz algebra LipαXdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Lip_{alpha }X$$end{document} is ideally Connes-amenable, whenever X is an infinite compact metric space and 0<α<1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$0