线性算子有界性的特征刻画

Characteristics of Depicting the Bounded Linear Operator

古典分析中的函数概念是指两个数集之间所建立的一种对应关系。现代数学的发展却要求建立两个任意集合之间的某种对应关系,即算子。算子是泛函分析中最重要的概念之一,研究算子的有界性是分析理论关注的首要问题,本文证明了关于线性算子有界性的一些等价命题。

Function in the classical analysis is established between two data sets. The development of modern mathematics needs to set up a corresponding relationship between two arbitrary collections,namely,operator. Operator is one of the most important concepts in functional analysis. The boundedness of the operator is a primary issue in the theory of analysis. This article gets some equivalent propositions about the boundedness of the linear operator.