A Characterization of Homomorphisms Between Banach Algebras  

作　　者：JianLianCUI JinChuanHOU 

机构地区：[1]DepartmentofMathematicalSciences,TsinghuaUniversity,Beijing100084P.R.China [2]DepartmentofMathematics,ShanxiTeachersUniversity,Linfen041004,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2004年第4期761-768,共8页数学学报（英文版）

基　　金：supported by NNSFC (10071046);PNSFS (981009);PYSFS(20031009);China Postdoctoral Science Foundation

摘　　要：We show that every unital invertibility preserving linear map from a von Neumann algebra onto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to a problem of Kaplansky for all von Neumann algebras.For a unital linear map Φ from a semi-simple complex 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.We show that every unital invertibility preserving linear map from a von Neumann algebra onto a semi-simple Banach algebra is a Jordan homomorphism;this gives an affirmative answer to a problem of Kaplansky for all von Neumann algebras.For a unital linear map Φ from a semi-simple complex 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.

关 键 词：Banach algebras HOMOMORPHISMS Jordan homomorphisms 

分 类 号：O177.5[理学—数学]