摘要
本文〔6〕讨论了Banach空间中抽象级数的收敛性,文〔7〕在Banach空间中构造并研究了抽象的幂级数;本文则在赋范空间中提出了囿变算子序列、一致囿变算子和算子级数收敛等概念,得出了算子级数收敛或一致收敛的一系列定理。
ln this paper we devolop some of the basic concepts, concerning the theory of. operator series on Banach spaces, which are the sequence of operators of(uniform)bounded variation, the operator-series and its (uniform)convergence, etc. At the same time we give several convergence tests of the series on Banach spaces.
关键词
BANACH空间
囿变算子序列
算子级数
Banach space, sequence of operators of bounded variation, ( uniformly ) convergence of operators-series.
