Home > Papers

 
 
On super weakly compact convex sets and representation of ${m swcc}(X)^*$
Cheng Lixin 1,Luo Zhenghua 2 *,Zhou Yu 1
1.Department of Mathematical Science, Xiamen University
2.Department of Mathematics, Huaqiao University
*Correspondence author
#Submitted by
Subject:
Funding: none
Opened online: 7 April 2011
Accepted by: none
Citation: Cheng Lixin,Luo Zhenghua,Zhou Yu.On super weakly compact convex sets and representation of ${m swcc}(X)^*$[OL]. [ 7 April 2011] http://en.paper.edu.cn/en_releasepaper/content/4419358
 
 
In this note, we give first that a characterization of super weakly compact convex sets of a Banach space $X$, namely, a sufficient and necessary condition for a closed bounded convex set $Ksubset X$ to be super weakly compact is that there exists a $w^*$ lower semicontinuous seminorm $p$ with $pgeqsigma_Kequivsup_{xin K}langlecdot,x angle$ such that $p^2$ is uniformly Fr'echet differentiable on each bounded set of $X^*$; and show then a representation theorem for the dual of the semigroup ${ m swcc}(X)$ consisting of all the nonempty super weakly compact convex sets of the space $X$.
Keywords:super weakly compact set; dual of normed semigroup; uniform Fr'echet differetiability; representation
 
 
 

For this paper
  • ● PDF (0B)
  • ● Revision 0 　　
  • ● Print this paper
  • ● Recommend this paper to a friend
  • ● Add to my favorite list

    Saved Papers

    Please enter a name for this paper to be shown in your personalized Saved Papers list

Tags
Add yours

Related Papers

Statistics
PDF Downloaded 255
Bookmarked 0
Recommend 5
Comments Array
Submit your papers