局部β-凸空间中的第二分离性定理及其共轭锥上的有界性定理(英文)

The Second Separation Theorem in Locally β-Convex Spaces and the Boundedness Theorem in Its Conjugate Cones

英文关键词:locally β-convex space  β-subseminorm  β-extreme point（set）  β-Minkowski functional  conjugate （topological） cone  subcomplete  U F - （U B- ）boundedness.

中文摘要:

      第一部分给出局部β－凸空间中的第二分离性定理和Ｍｉｎｋｏｗｓｋｉ定理及Ｋｒｅｉｎ－Ｍｉｌｍａｎ定理等；第二部分得到其共轭锥上Ｕ Ｆ－有界与Ｕ Ｂ－有界等价的充要条件为原空间是次完备的．

英文摘要:

      This paper deals with the locallyβ-convex analysis that generalizes the locally convex analysis. The second separation theorem in locallyβ-convex spaces, the Minkowski theorem and the Krein-Milman theorem in theβ-convex analysis are given. Moreover, it is obtained that the U F-boundedness and the U B-boundedness in its conjugate cone are equivalent if and only if X is subcomplete.