比较判别法在泛函分析中的应用

Applications of the Comparison Test Principle in Functional Analysis

在数学分析中,比较判别法是判断正项级数收敛性的一种基础的方法.借鉴比较判别法的思想,应用于泛函分析中用来判别p次可和序列空间上的加权移位算子是否为Cesàro有界的或绝对Cesàro有界的.

In Mathematical Analysis,the comparison test principle is a basic method to prove the convergence of the positive series.In the article,we use the spirit of the comparison test principle to the problems in Functional Analysis.We give a discriminated method of the Cesàro boundedness of weighted backward shift operators on the space of p summable sequnces.