Home > Papers

 
 
Reflexivity and reducibility of operators related to invariant subspace problem
Ji You Qing *,Xu Xinjun
Mathematics school of Jilin University
*Correspondence author
#Submitted by
Subject:
Funding: 教育部博士点基金等（No.20050183002）
Opened online: 7 January 2009
Accepted by: none
Citation: Ji You Qing,Xu Xinjun.Reflexivity and reducibility of operators related to invariant subspace problem[OL]. [ 7 January 2009] http://en.paper.edu.cn/en_releasepaper/content/27437
 
 
The well-known invariant subspace problem is A long-standing problem in operator theory,which has been to determine whether every (bounded linear) operator $T$ on a Banach space $X$ must have a nontrivial invariant subspace. every reducible subspace of $T$ is invariant subspace of $T$ too. We show that, for some Banach space operators $T$,( {\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\it bi-crystal} operator) the following statements are equivalent. (1) There exists a nontrivial invariant subspace of $T$. (2) $T$ is Banach reducible. (3) $T$ is reflexive. And we show that if $A\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\sim A \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\bigoplus A$, then $A$ is reflexive.
Keywords:Banach reducible;reflexive;crystal;inflation
 
 
 

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 379
Bookmarked 0
Recommend 5
Comments Array
Submit your papers