| ON THE PRODUCT OF GATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES |
| |
| 摘 要： |
|
| 关 键 词： | 局部凸函数 Gateaux可微空间 连续性 弱拓扑 数学物理 |
| 收稿时间： | 23 September 2002 |
ON THE PRODUCT OF GÂTEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES |
| |
| Institution: | 1. Laboratoire d’Analyse Non linéaire et Mathématiques Appliquées, Université de Tlemcen, Faculté des Sciences, Département de Mathématiques, Algérie;2. UMI IRD 209 UMMISCO Centre IRD de lIle de France 32 Avenue Henri Varagnat, 93143 Bondy Cedex, France;3. Sorbonne Universités, UPMC Univ Paris 06, France |
| |
| Abstract: | A locally convex space is said to be a Gâteaux differentiability space (GDS) provided every continuous convex function defined on a nonempty convex open subset D of the space is densely Gâteaux differentiable in D. This paper shows that the product of a GDS and a family of separable Fréchet spaces is a GDS, and that the product of a GDS and an arbitrary locally convex space endowed with the weak topology is a GDS. |
| |
| Keywords: | Convex function locally convex space Gâteaux differentiability space 46B20 46G05 26E15 |
| 本文献已被 ScienceDirect 等数据库收录！ |
