关于Gelfand-Mazur型的两个定理(英文)

On Two Gelfand-Mazur Type Theorems

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.