Acta mathematica scientia,Series B ›› 2005, Vol. 25 ›› Issue (3): 395-400.

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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)

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

CLC Number: 

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