随机级数的S-可和性与本性收敛

The S-sums and essential convergence of random series

先研究了Banach空间中的向量级数收敛和S-可和的关系;然后得到了一个好的结果:一般的复级数都存在一个求和阵S,使它可和;最后在此基础上,研究了随机级数S-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.

At first, studies the relation between convergence and S - sums of vector series in a Banach space. Then it obtains a good result： there exists a summation matrix which makes general complex series are S - summable. Finally, by the aboving result, it studies the relation bewteen S - summability and essential convergence of random series, and obtains necessary and sufficient conditions on essential convergence of random series.