华南师范大学学报(自然科学版)
華南師範大學學報(自然科學版)
화남사범대학학보(자연과학판)
JOURNAL OF SOUTH CHINA NORMAL UNIVERSITY (NATURAL SCIENCE EDITION)
2014年
1期
7-10
,共4页
对合算子%线性组合%幂等%三次幂等
對閤算子%線性組閤%冪等%三次冪等
대합산자%선성조합%멱등%삼차멱등
involutory operator%linear combination%idempotent%tripotent
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。
研究瞭冪等、對閤、三次冪等算子線性組閤的遺傳性質;利用算子分塊技巧,對這類問題所涉及的各種組閤給齣瞭統一的證明;得到瞭交換三次冪等算子線性組閤仍為三次冪等的充要條件;最後,討論瞭所得結論的應用範圍,推廣、髮展瞭原有的一些定理。
연구료멱등、대합、삼차멱등산자선성조합적유전성질;이용산자분괴기교,대저류문제소섭급적각충조합급출료통일적증명;득도료교환삼차멱등산자선성조합잉위삼차멱등적충요조건;최후,토론료소득결론적응용범위,추엄、발전료원유적일사정리。
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 nec-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-tions of multi-commutative potents .Some known results are generalized with a short proof .