A Characterization of Homomorphisms Between Banach Algebras

被引：0
作者：
Jian Lian CUI Department of Mathematical SciencesTsinghua UniversityBeijing PRChina and Department of MathematicsShanxi Teachers University Linfen PRChina Jin Chuan HOU Department of MathematicsShanxi Teachers UniversityLinfen PRChina and Department of MathematicsShanxi UniversityTaiyuan PRChina [100084 ,41004 ,41004 ,30000 ]
机构：
来源：
ActaMathematicaSinica(EnglishSeries) | 2004年 / 20卷 / 04期
关键词：
Banach algebras; Homomorphisms; Jordan homomorphisms;
D O I：
暂无
中图分类号：
O153 [抽象代数（近世代数）];
学科分类号：
070104 ;
摘要：
<正> We show that every unital invertibility preserving linear map from a von Neumann algebraonto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to aproblem of Kaplansky for all von Neumann algebras.For a unital linear map Φ from a semi-simplecomplex Banach algebra onto another,we also show that the following statements are equivalent:(1)Φ is an homomorphism;(2)Φ is completely invertibility preserving;(3)Φ is 2-invertibility preserving.
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页码：761 / 768
页数：8
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