随机级数的T-可和性与本性收敛

T-Summability and Essential Convergence of Random Series

研究了Banach空间中向量级数的收敛性与T-可和性的关系,得出了结果:一般的复级数都存在一个求和阵T,使之为T-可和,并在此基础上,研究了随机级数的T-可和性与本性收敛的关系,得到了随机级数本性收敛的充要条件.

This paper studies the relationship between the convergence and T-summability of vector series in a Banach space firstly,and then proves that there exists a T-summation matrix which makes general complex series are T-summable.Finally,according to the above result,it studies the relation bewteen T-summability and essential convergence of random series,and obtains necessary and sufficient conditions on essential convergence of random series.