Subseries Convergence and Unconditionally Convergence of Compact Operator Series

Let(E,r)bealocallyconvexHausdorfftopologicalvectorspace.AseriesZxiinEissaidtobesubseriesr-convergent(-s.c.),ifforeachstrictlyincreasingsequence{n,}inN,theseriesZx"'isT-convergent.TheseriesZx,issaidtobeunconditionallyr-convergent(r-u.c.),ifforeachpermutationffofN,theseriesZx,<,,ls.,r-convergence.rheseriesZx,issaidtobesubseriesunconditional1yT-convergent(r-s.u.c.)ifforeachstrictlyincreasingseqtience{n,}inN,theseriesZx.,isunconditionallyr-convergent.If(E,r)isasequentiallycompletespace,thenT…     

关于Orlicz-Pettis定理(英文)

本文实质性的改进了著名的Orlicz-Pettis定理     

序列空间的σ—对偶

本文研究了两类重要序列空间的σ－对介,证明了局部凸空间的某些拓扑性质可用σ－对偶予以刻划,进一步地,一个Schur型结果和一个矩阵映象的自连续性结果被建立了。