最强Orlicz-Pettis拓扑

The Strongest Orlicz-Pettis Topology

引进了lp（p≥1）空间的子集是本性紧概念，借此给出了抽象对偶系统（E，F）中最强Orlicz－Petits拓扑SOP（E，F）以及产生该拓扑的最大映射集族的表示．利用此结果搞清楚了现有两种Orlicz－Petits拓扑即Dierolf拓扑（M）和Twed－dle拓扑（E，T’）的确切意义以及它们之间的相互关系．指出了的最大性所蕴涵的理论意义和应用价值．证实了σ（F，E）-条件紧集和σ（F，E）-可数紧集都含于中。进而实质性地改进了矢位测度论中的Graves－Rness定理、抽象函数论中的Thomas定理等重要结果．

By introducing the concept of essentially compact subsets of the spaces lp(p ≥ 1), the strongest Orlicz-Pettis topology and the largest mappings family F whichyielded this topology in abstract duality pair (E,F) are obtained. Through usingthese results, the relationship between Dierolf topology F(M*) and Tweddle toplogyT(E, T′) has been shown. It is also proved that both conditionally o(F, E)-sequentiallycompact subsets of F and o(F, E)-countably compact subsets of F belong to the largestmappings family f. Thus, some famous theorems, such as the Graves-Ruess theorem onvector measures, the Thomas theorem on abstract function theory, etc., are improvedsubstantially.