应用泛函分析学报
應用汎函分析學報
응용범함분석학보
ACTA ANALYSIS FUNCTIONALIS APPLICATA
2002年
4期
317-320
,共4页
零因子%实C*-代数%厄米Banach*-代数
零因子%實C*-代數%阨米Banach*-代數
령인자%실C*-대수%액미Banach*-대수
zero divisors%real C*-algebra%hermitian Banach*-algebra
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.
證明瞭兩箇Gelfand-Mazur型的定理. 其一是:設A是一單位C*-代數,AH()R,且噹h∈AK時,eh具有凸譜集. 則A()C. 這一結果迴答瞭Bhatt等人的問題,給齣瞭他們的結果在實情形中的結論.其二,部分地迴答瞭Bhatt等人的另一箇問題,結果是:設A是一複單位阨米Banach*-代數. 假設(I)對任意x∈AH,譜集σA(x)的內部是空集,且C\σA(x)是連通的;(ii)A沒有非零零因子. 則A同構到C.
증명료량개Gelfand-Mazur형적정리. 기일시:설A시일단위C*-대수,AH()R,차당h∈AK시,eh구유철보집. 칙A()C. 저일결과회답료Bhatt등인적문제,급출료타문적결과재실정형중적결론.기이,부분지회답료Bhatt등인적령일개문제,결과시:설A시일복단위액미Banach*-대수. 가설(I)대임의x∈AH,보집σA(x)적내부시공집,차C\σA(x)시련통적;(ii)A몰유비령령인자. 칙A동구도C.
Two Gelfand-Mazur type theorems are proved. One is: Let A be a real unital C*-algebra, AH()R, and eh 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.
