摘要
设F是一个域,V是F上的一个向量空间,α是V上的一个线性变换,m是一个大于1的正整数。若V上的线性变换χ满足χ^(m)=α,则称χ是α的一个m次根。借助主理想整环上有界模的Prüfer-Baer定理,研究无限维复向量空间上代数线性变换,给出了α的一个m次根可表示为α的多项式的局部条件和整体条件,所得结果深化了矩阵分析里的相关内容。
Let F be a field,V is a vector space on F,α is a linear transformation on V and m is a positive integer greater than 1.If a linear transformation χ on V satisfies χ^(m)=α,then χ is called an m-th root of.In this paper,using the Prüfer-Baer theorem of bounded modules over the principal ideal domain,we study the linear transformation which is algebraically on infinite dimensional complex vector spaces,and give the localααand global conditions under which an m-th root of can be expressed as a polynomial in.The obtained results deepen the related results in the matrix analysis.
作者
王涵
赵静
刘合国
WANG Han;ZHAO Jing;LIU Heguo(School of Mathematics and Statistics,Hainan University,Haikou 570228,China)
基金
国家自然科学基金项目(12171142)。
