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| 最强Orlicz-Pettis拓扑 | |
| 引用本文： | 李容录,崔成日,CHO Min-Hyung.最强Orlicz-Pettis拓扑[J].数学学报,2000,43(1):9-16. |
| 作者姓名： | 李容录 崔成日 CHO Min-Hyung |
| 作者单位： | 1. 哈尔滨工业大学数学系,黑龙江,哈尔滨,150001 2. 延边大学数学系,吉林,延吉,130002 3. 金乌工科大学应用数学系,韩国 |
| 基金项目： | 黑龙江省自然科学基金，吉林省教委自然科学基金 |
| 摘 要： | 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． |
| 关 键 词： | Orlicz－Pettis拓扑 本性紧 抽象对偶系统 |
The Strongest Orlicz-Pettis Topology |
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| LI Rong-lu,CUI Cheng-ri,CHO Min-Hyung.The Strongest Orlicz-Pettis Topology[J].Acta Mathematica Sinica,2000,43(1):9-16. | |
| Authors: | LI Rong-lu CUI Cheng-ri CHO Min-Hyung |
| Institution: | LI Rong-lu(Department of Mathematics, Harbin Institute Of Technology, Harbin 15000l, P. R. China)CUI Cheng-ri(Department of Mathetnatics, Yanbian Unviersity, Yanji 133002, P. R. China)CHO Min-Hyung(Department of Mathematics, Kum-Oh Universitg of Technolog |
| Abstract: | 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. |
| Keywords: | Orlicz-Pettis topology Essentially compact Abstract duality pair |
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