n×n阵列到自身的有界线性算子族问题

The problem about family of bounded linear operator from n×n matrices to itself

在泛函分析的基础理论中,人们很少去过问n×n阵全体An×n的线性空间问题、范数问题,特别是An×n到自身的有界线性算子的结构,以及有界线性算子的范数问题,如文献[1～4].本文给出了An×n的基底、An×n是线性空间、An×n上多个范数及An×n到自身的线性算子的结构以及算子的范数估计.

There were few results about linear spaces of n×n matrices and norms for them in fundamental theories of functional analysis such as the structure of bounded linear operators from A_(n×n) to itself and the problem about norms of bounded linear operator . In this paper, we give a basis of A_(n×n), show that A_(n×n) is a linear space and give several norms on A_(n×n). Besides, we obtain the structure of linear operators which from A_(n×n) to itself and the evaluation of norms of operations.