关于R^n到R^n的有界线性算子族问题

The problem about family of bounded linear operator from R^n to R^n itself

在建立Rn上4个范数的基础上,对(Rn,‖·‖i)到(Rn,‖·‖j)的有界线性算子族中的每个有界线性算子Aij(i,j=1,2,p,∞)的范数进行估计,用以丰富泛函分析的基础理论,同时为相关学科的科研和教学人员提供参考资料.

In this paper authors set up the four norms on R^n. Then, estimate that every bounded linear operator A_(ij)(i,j=1,2,p,∞), which is in family of bounded linear operators from (R^n,‖·‖_i) to ((R^n,‖·‖_j).) This is a development of basical theory and gives a reference to researchers and teachers.