Fredholm算子指标在紧扰动、小扰动下的不变性  

The Invariant of the Index of the Fredholm Operator Under Compact Perturbation & Small Perturbation

作　　者：陈永翠 

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《湖北民族学院学报（自然科学版）》2017年第4期417-419,422,共4页Journal of Hubei Minzu University(Natural Science Edition)

基　　金：重庆市研究生科研创新项目(YKC16001)

摘　　要：主要研究了Fredholm算子及其指标分别在紧扰动和小扰动下的变化情况;验证了抽象指标与传统指标本质相同;并利用开集、同态映射和Fredholm算子的性质对Fredholm算子及其指标分别在紧扰动和小扰动下的不变性给出了相应的证明.In this article, we studied the changes of Fredholm operators and its index under compact per-turbation ＆ small perturbation. We also proved that the classical index i and the abstract index j are essen-tially the same.At last,we gave the proofs of invariation by the properties of open set, homomorphic map- ping and Fredholm operators.

关 键 词：紧算子 FREDHOLM算子 紧扰动 小扰动 不变性 

分 类 号：O177.1[理学—数学]