摘要
不变子空间问题是算子理论中一个著名的问题,为了把Abramovich等人关于紧算子的不变子空间相关结果推广到AM-紧算子,本文对Banach格上AM-紧算子的性质做了比较深入的探讨.主要研究了其控制性质与格性质,并给出结果:若Banach格E上算子T、S满足0≤S≤T,T是AM-紧算子,则S2是AM-紧算子,AM-紧算子的一些其他性质也进行了相关讨论.
The Invariant Subspace Problem is a famous problem in the operator theory. For generalizing the results in Abramovich＇s paper about the positive compact operators, this paper is devoted to the properties of AM-compact operators on Banach lattice. Its domination and lattice property is given, and it is proven that if a positive operator on a Banach lattice is dominated by an AM-compact operator, then its square is also an AM-compact operator.Some relative properties are also discussed.
出处
《信阳师范学院学报（自然科学版）》
CAS
北大核心
2007年第1期14-16,共3页
Journal of Xinyang Normal University(Natural Science Edition)
基金
四川省科技厅基础研究项目(05JY029-006-5)
