The Reduced Minimum Modulus in <Emphasis>C</Emphasis><Superscript>*</Superscript>-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

*The Reduced Minimum Modulus in C-Algebras**

Authors:	Yifeng?Xue author-information" > author-information__contact u-icon-before icon--email-before" > mailto:yfxue@math.ecnu.edu.cn,xyf@public.sta.net.cn" title=" yfxue@math.ecnu.edu.cn,xyf@public.sta.net.cn" itemprop=" email" class=" gtm-email-author" >Email author

Affiliation:	(1) Department of Mathematics, East China Normal University, Shanghai, 200062, P.R. China

Abstract:	We define the reduced minimum modulus $gamma _{mathcal {A}} (a)$ of a nonzero element a in a unital C ^-algebra by $gamma _{mathcal {A}} (a) = rm{inf}{parallel a-b parallel \| rm{AL}({it a})subsetneqq AL({it b}), b in {mathcal {A}}}$ . We prove that $gamma _{mathcal {A}} (a) = rm{inf}{lambda \| lambda in sigma((a^{}a)^{frac{1}{2}})setminus {0}}$ . Applying this result to and its closed two side ideal , we get that dist $(a, Phi^{c}_{l}({mathcal {A}})) = rm{min}{lambda \| lambda in sigma(pi((a^{*}a)^{frac{1}{2}}))}$ , and $gamma _{mathcal {B}}(pi(a)) = text{sup}{gamma _{mathcal {A}}(a + k) \| k in {mathcal {I}}}$ for any if RR = 0, where and is the quotient homomorphism and $Phi^{c}_{l} ({mathcal{A}}) ={a in {mathcal {A}} \| pi(a) text{is not left invertible in},{mathcal {B}}}$ . These results generalize corresponding results in Hilbert spaces.

Keywords:	46L05
本文献已被 SpringerLink 等数据库收录！