Von Neumann Regularity and Quadratic Conorms in JB^＊-triples and C^＊-algebras

作     者：María BURGOS El Amin KAIDI Antonio Morales CAMPOY Antonio M.PERALTA Maribel RAMíREZ 

作者机构：Department of Algebra and Mathematical Analysis University of Almería 04120 Almería Spain Department of Mathematical Analysis University of Granada 18071 Granada Spain Department of Algebra and Mathematical Analysis University of Almerǐa 04120 Almería Spain 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2008年第24卷第2期

页      面：185-200页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：I+D MEC Projects No.MTM 2005-02541,MTM 2004-03882 Junta de Andalucfa Grants FQM 0199,FQM 0194,FQM 1215 the PCI Project No.A/4044/05 of the Spanish AECI 

主　　题：von Neumann regularity quadratic conorm C^*-algebra JB^*-triple triple spectrum 

摘      要：We revise the notion of von Neumann regularity in JB^＊-triples by finding a new characterisation in terms of the range of the quadratic operator Q（a）. We introduce the quadratic conorm of an element a in a JB^＊-triple as the minimum reduced modulus of the mapping Q（a）. It is shown that the quadratic conorm of a coincides with the infimum of the squares of the points in the triple spectrum of a. It is established that a contractive bijection between JBW^＊-triples is a triple isomorphism if, and only if, it preserves quadratic conorms. The continuity of the quadratic conorm and the generalized inverse are discussed. Some applications to C^＊-algebras and von Neumann algebras are also studied.