Trace and spectrum preserving linear mappings in Jordan-Banach algebras

被引：0
作者：
Bernard Aupetit
机构：
[1] Université Laval,Département de Mathématiques et de Statistique Faculté des Sciences et de Génie
来源：
Monatshefte für Mathematik | 1998年 / 125卷
关键词：
17C65; 46H70; Jordan-Banach algebra; spectrum preserving mapping; Jordan isomorphism; socle; trace;
D O I：
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学科分类号：
摘要：
In the first section we define the trace on the socle of a Jordan-Banach algebra in a purely spectral way and we prove that it satisfies several identities. In particular this trace defines the Faulkner bilinear form. In the second section, using analytic tools and the properties of the trace, we prove that a spectrum preserving linear mapping fromJ ontoJ1, whereJ andJ1 are semisimple Jordan-Banach algebras, is not far from being a Jordan isomorphism. It is in particular a Jordan isomorphism ifJ1 is primitive with non-zero socle.
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页码：179 / 187
页数：8
相关论文
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