Real rank and squaring mappings for unital <IMG BORDER="0" SRC="/proc/2004-132-03/S0002-9939-03-07102-8/gif-title0/img1.gif" >-algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Real rank and squaring mappings for unital -algebras

Authors:	A Chigogidze A Karasev M Rø rdam

Institution:	Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada ; Department of Mathematics and Statistics, University of Saskatchewan, McLean Hall, 106 Wiggins Road, Saskatoon, SK, S7N 5E6, Canada ; Department of Mathematics, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark

Abstract:	It is proved that if is a compact Hausdorff space of Lebesgue dimension $\dim(X)$ , then the squaring mapping $\alpha_{m} \colon \left( C(X)_{\mathrm{sa}}\right)^{m} \to C(X)_{+}$ , defined by $\alpha_{m}(f_{1},\dots ,f_{m}) = \sum_{i=1}^{m} f_{i}^{2}$ , is open if and only if $m -1 \ge \dim(X)$ . Hence the Lebesgue dimension of can be detected from openness of the squaring maps $\alpha_m$ . In the case it is proved that the map $x \mapsto x^2$ , from the selfadjoint elements of a unital $C^{\ast}$ -algebra into its positive elements, is open if and only if is isomorphic to for some compact Hausdorff space with $\dim(X)=0$ .

Keywords:	Real rank bounded rank Lebesgue dimension

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文