摘要
本文构造了一类算子A,并对其中的算子进行了谱分析.同时指出了A中算子成为有界的、紧的或自伴的充要条件.在此基础上,构造了一些颇具特性的算子,从而数值函数与抽象函数的显著性差异可窥见一斑.
This paper constructs a class A of operators and gives a spectral analysis of an operator in it. And it presents the necessary and sufficient c-ondition under which an operator in A becomes compact or self - adjoint.
关键词
闭子空间
直交和
点谱
紧算子
自伴算子
谱系
有界性
数值函数
抽象函数
Orthogonal direct sum of closed subspaces
Point spectrum
Spectrum, Compact operator, Self-adjoint operator
Hierarchy.
