关于Gelfand-Mazur型的两个定理(英文)  

On Two Gelfand-Mazur Type Theorems

作　　者：李忠艳[1] 李民丽[2] 

机构地区：[1]华北电力大学(北京)科学与工程计算研究所,北京102206 [2]首都师范大学数学系,北京100037

出　　处：《应用泛函分析学报》2002年第4期317-320,共4页Acta Analysis Functionalis Applicata

摘　　要：证明了两个Gelfand.Mazur型的定理.其一是:设A是一单位C*-代数,AH≌R,且当h∈Ak时,eh具有凸谱集.则A≌C.这一结果回答了Bhatt等人的问题,给出了他们的结果在实情形中的结论.其二,部分地回答了Bhatt等人的另一个问题,结果是:设A是一复单位厄米Banach*-代数.假设(i)对任意x∈AH,谱集σA(x)的内部是空集.且C\σA(x)是连通的;(ii)A没有非零零因子.则A同构到C.Two Gelfand-Mazur type theorems are proved. One is; Let A be a real unital C*-algebra, AH≌ R, and eA has convex spectrum whenever h ?AK, then A≌C, which provides an answer to one question of Bhatt and others and gives the real analogue of one result of them. Another is : Let A be a complex hermitian Banach *-algebra with identity I. Assume that (1) The interior of the spectrum σA.(x) is an empty set, and C\σA(x) is connected, for any x∈AH. (2) A has no nonzero divisor of zero. Then A is isomorphic to C. This result answers partially another question of Bhatt and others.

关 键 词：Gelfand-Mazur型 零因子 实C^＊-代数 厄米Banach^＊-代数 

分 类 号：O177.1[理学—数学]