幂等算子组合的可逆性  

The Invertibility of Combinations of Idempotents

作　　者：谢涛[1] 左可正[1] 余盛利[1] 陈引兰[1] 

机构地区：[1]湖北师范学院数学与统计学院,湖北黄石435002

出　　处：《广西民族大学学报（自然科学版）》2012年第3期48-51,共4页Journal of Guangxi Minzu University ：Natural Science Edition

基　　金：湖北省教育厅重点项目(D20122202);湖北省教育厅青年项目(B20122203)

摘　　要：讨论了希尔伯特空间上的两个不同的幂等算子P、Q的组合aP+bQ-cPQ的可逆性问题,利用幂等算子的性质和空间分解的技巧证明了aP+bQ-cPQ的可逆性与系数的选取无关,其中a,b,c∈瓘,ab≠0,a+b-c≠0.而且构造反例说明该结果不能推广到aP+bQ-cPQ-dQP的情形.Discussed the problem of invertibility of combinations of two different idempotent operators P,Q on a Hilbert space. The invertibility of aP ＋ bQ-cPQ are independent choice of coefficients, where a, b, c ∈ C ,ab ≠ 0 ,a ＋b ≠c which was proved by using the properties of idempotent operators and the techniques of space decomposition. Moreover, some counter examples were constructed to denote that the result can not be generalized to the case aP ＋ bQ-cPQ-dQP .

关 键 词：幂等算子 可逆性 幂等算子的组合 

分 类 号：O152.2[理学—数学]