Pettis积分与Frechet空间的核性

Pettis积分与Frechet空间的核性 PETTIS INTEGRATION AND NUCLEARITY IN FRECHET SPACES 侯友良 Hou Youliang Liu Peide 1 first-author 刘培德 1 武汉大学数学系 武汉大学数学系 Department of Mathematics,Wuhan University Department of Mathematics,Wuhan University 本文在 Frechet 空间中讨论了 Bochner 积分和 Pettis 积分的若干性质,对可积函数空间定义了 Bochner 拓扑（平均拓扑）和 Pettis 拓扑.利用这两种拓扑之间的关系以及势和一致势的关系给出了空间具有核性的若干等价条件. In this paper,we discussed some properties of Bochner integration and Pettis integration in Frechet space and defined Bochner topology and Pettis topology on the space of integrable functions.We gave some equivalent con- dition for a Frechet space to be a nuclear spate by means of relation betwen the two topologies. Frechet 空间 Bochner 积分 Pettis 积分 核性 Frechet space Bochner integration Pettis integration nuclea rity O177.3;O211.6 1992-02-01 2021-04-01 2