ON THE PRODUCT OF GTEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES 被引量：1

ON THE PRODUCT OF GTEAUX DIFFERENTIABILITY LOCALLY CONVEX SPACES

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

作者沈喜生程立新

机构地区 School of Mathematical Sciences Xiamen University

出处《Acta Mathematica Scientia》 SCIE CSCD 2005年第3期395-400,共6页 数学物理学报（B辑英文版）

基金 Supported by the NSF of China (10071063 and 10471114)

关键词 Convex function locally convex space Gateaux differentiability space Convex function, locally convex space, Gateaux differentiability space

分类号 O174.13 [理学—基础数学] O411.1 [理学—理论物理]

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2005年第3期

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