华中师范大学学报（自然科学版）2012，Vol.46Issue(6)：649-652,4.
幂等算子组合的指数及Fredholm性
The index and Fredholmness of combinations of idempotent operators
摘要
Abstract
If P/Q are two different idempotent operators on Hilbert space, Du, etc. in 2006 proved that the invertiblilty of linear combinations of aP-hbQ is independent of the choice of coefficients, where a, b∈C, ab≠0, a +b≠0. In the present note, this results are strengthened by showing that the index and Fredholmness of aP+bQ-cPQ are also independent of the choice of coefficients, where a,b,c∈C, ab≠0 , a+b—c≠0. Moreover, some examples are constructed to denote that the above result can not be generalized to the case aP+bQ- cPQ-dQP.关键词
幂等算子/指数/Fredholm性/组合Key words
idempotent operator/ index/ Fredholmness/ combination分类
数理科学引用本文复制引用
谢涛,左可正..幂等算子组合的指数及Fredholm性[J].华中师范大学学报（自然科学版）,2012,46(6):649-652,4.基金项目
湖北省教育厅科研重点项目(D20122202) （D20122202）
湖北省教育厅青年项目(B20122203) （B20122203）
