| Von Neumann Regularity and Quadratic Conorms in JB^＊-triples and C^＊-algebras |
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| 作者姓名： | Maria BURGOS ;E Amin KAIDI ;Antonio Morales CAMPOY ;Antonio M. PERALTA ;Maribel RAMIREZ |
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| 作者单位： | [1]Department of Algebra and Mathematical Analysis, University of Almeria, 04120 Almeria, Spain; [2]Department of Mathematical Analysis, University of Granada, 18071 Granada, Spain |
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| 基金项目： | Authors partially supported by I＋D MEC Projects No. MTM 2005-02541, MTM 2004-03882, Junta de An-dalucia Grants FQM 0199,FQM 0194, FQM 1215 and the PCI Project No. A/4044/05 of the Spanish AECI |
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| 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.
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| 关 键 词： | C^＊代数 三倍光谱 代数学 冯·诺尔曼规则 |
| 文章编号： | 10.1007/s10114-007-0985-X |
| 收稿时间： | 31 March 2006 |
| 修稿时间： | 6 December 2006 |
Von neumann regularity and quadratic conorms in JB*-triples and C*-algebras |
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| Maria BURGOS,;E Amin KAIDI,;Antonio Morales CAMPOY,;Antonio M. PERALTA,;Maribel RAMIREZ.Von neumann regularity and quadratic conorms in JB*-triples and C*-algebras[J].Acta Mathematica Sinica,2008,24(2):185-200. |
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| Authors: | María Burgos Amin El Kaidi Antonio Morales Campoy Antonio M Peralta Maribel Ramírez |
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| Institution: | (1) Department of Algebra and Mathematical Analysis, University of Almería, 04120 Almería, Spain;(2) Department of Mathematical Analysis, University of Granada, 18071 Granada, Spain;(3) Department of Algebra and Mathematical Analysis, University of Almería, 04120 Almería, Spain |
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| Abstract: | 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.
Authors partially supported by I+D MEC Projects No. MTM 2005-02541, MTM 2004-03882, Junta de Andalucía Grants FQM 0199,FQM
0194, FQM 1215 and the PCI Project No. A/4044/05 of the Spanish AECI |
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| Keywords: | von Neumann regularity quadratic conorm C*-algebra JB*-triple triple spectrum |
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