摘要
设a=(a_1,…,a_n)是Banach空间X上的交换算子组,a的Taylor联合谱记为在Sp(a,x).本文中,联合谱的一部分被定义为混合谱,并用实例验证了混合谱的存在性,随后用摄动的方法讨论了联合谱及混合谱的一些性质,证明了在Hilbert空间上的交换算子对的混合谱是一个开集,而在一般情形下,得到了一个关于Taylor联合谱边界的性质.
Let a be a commuting n-tuple of operators.The concept of mixed spectrum σ_m(a)of a is introduced and the existence of mixed spectrum with some examples is illustratod.The joint spectrum and the mixed spectrum are discussed with the method of perturbation.Results show that the mixed spectrum of two commuting operators is an open set.For n>2, the mixed spectrum σm(a) is divided into type I σ_(m??)(a) and type II σ_(m??)(a), and it is proved that σ_(m??)(a)is an open set, from which a property of the boundary of Taylor′s joint spectrum is obtaintd.
出处
《华东师范大学学报（自然科学版）》
CAS
CSCD
1990年第2期8-13,共6页
Journal of East China Normal University(Natural Science)
关键词
交换算子组
联合谱
分类
混合谱
commuting n-tupleof operators joint spectrum classification mixed spectrum perturbation
