数学物理学报(英文版) ›› 2005, Vol. 25 ›› Issue (3): 395-400.

• 论文 • 上一篇    下一篇

ON THE PRODUCT OF G\^ATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

沈喜生|程立新   

  1. School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 出版日期:2005-07-20 发布日期:2005-07-20
  • 基金资助:

    Supported by the NSF of China (10071063 and
    10471114)

ON THE PRODUCT OF G\^ATEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

 CHEN Chi-Sheng, CHENG Li-Xin   

  • Online:2005-07-20 Published:2005-07-20
  • Supported by:

    Supported by the NSF of China (10071063 and
    10471114)

摘要:

A locally convex space is said to be a Gˆateaux differentiability space (GDS)
provided every continuous convex function defined on a nonempty convex open subset D
of the space is densely Gˆateaux differentiable in D.This paper shows that the product of
a GDS and a family of separable Fr´echet 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.

Abstract:

A locally convex space is said to be a Gˆateaux differentiability space (GDS)
provided every continuous convex function defined on a nonempty convex open subset D
of the space is densely Gˆateaux differentiable in D.This paper shows that the product of
a GDS and a family of separable Fr´echet 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.

Key words: Convex function locally convex space Gˆateaux differentiability space

中图分类号: 

  •