拟平移不变拓扑锥与局部β-凸空间的共轭锥  

Quasi-translation Invariant Topological Cones and TheConjugate Cones of Locally β-Convex Spaces

作　　者：王见勇[1] 

机构地区：[1]常熟高等专科学校数学系,江苏常熟215500

出　　处：《数学的实践与认识》2003年第1期89-97,共9页Mathematics in Practice and Theory

摘　　要：[1]中提出的局部β-凸分析问题从本质上来说是一种非线性凸分析问题 .为了刻画和研究局部β-凸空间 X的共轭锥 X*β ,本文在抽象凸锥上引进具有拟平移不变性质的拓扑结构 ,第一部分重点研究局部生成拓扑锥与赋范拓扑锥 .第二部分将这两种拓扑锥的一般理论应用于局部 β - 凸空间的共轭锥 X*β 的研究 ,得到 (X*β,U| A)与 (X*β ,‖‖ )的局部生成性与完备性定理等 .The β-convex analysis introduced by is a sort of nonlinearly convex analysis. In this paper, for the purpose of studying the conjugate cone X* β of locallyβ-convex space X, we introduce quasi-translation invariant topological structure on convex cones. The locally generated topological cones and the normed topological cones are studied at first. Making use the theories of quasi-translation invariant topological cones to the studying of locally β-convex analysis, the locally generated property and the completeness of (X* β, U|A) and (X* β,‖ ‖) are obtained at last.

关 键 词：拟平移不变拓扑锥 局部生成拓扑锥 赋范拓扑锥 局部Β-凸空间 共轭锥 一致空间 

分 类 号：O174.13[理学—数学]