三次幂等算子线性组合的遗传性质  

Revisitation of the Inheritance of Linear Combinations of Tripotent,Idempotent and Involutory Operators

作　　者：邓春源[1] 

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《华南师范大学学报（自然科学版）》2014年第1期7-10,共4页Journal of South China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11171222);教育部博士点新教师基金项目(20094407120001)

摘　　要：研究了幂等、对合、三次幂等算子线性组合的遗传性质;利用算子分块技巧,对这类问题所涉及的各种组合给出了统一的证明;得到了交换三次幂等算子线性组合仍为三次幂等的充要条件;最后,讨论了所得结论的应用范围,推广、发展了原有的一些定理.The inheritance of linear combinations of idempotent, involutory and tripotent operators are studied. U- sing block operator matrix methods, a universal proof of this kind of combinations is given. The sufficient and nee- essary conditions such that a linear combination of mutually commutative tripotent operators is tripotent are ob- tained. At last, this problem is revisited. It shows that this method is very powerful in dealing with linear combina- tion~ of multi-commutative potents. Some known results are generalized with a short proof.

关 键 词：对合算子 线性组合 幂等 三次幂等 

分 类 号：O177.1[理学—数学]