期刊文献+

Possibly non-unital operator system structures on a possibly non-unital function system

Possibly non-unital operator system structures on a possibly non-unital function system
原文传递
导出
摘要 In this paper, we first give the definition of possibly non-unital function system, which is a characterization of the self-adjoint subspace of the space of continuous functions on a compact Hausdorff space with the induced order and norm structure. Similar to operator system case, we define the unitalization of a possibly non-unital function system. Then we construct two possibly non-unital operator system structures on a given possibly non-unital function system, which are the analogues of minimal and maximal operator spaces on a normed space. These two structures have many interesting relations with the minimal and maximal operator system structures on a given function system. In this paper, we first give the definition of possibly non-unital function system, which is a characterization of the self-adjoint subspace of the space of continuous functions on a compact Hausdorff space with the induced order and norm structure. Similar to operator system case, we define the unitalization of a possibly non-unital function system. Then we construct two possibly non-unital operator system structures on a given possibly non-unital function system, which are the analogues of minimal and maximal operator spaces on a normed space. These two structures have many interesting relations with the minimal and maximal operator system structures on a given function system.
作者 Jianze LI
出处 《Frontiers of Mathematics in China》 SCIE CSCD 2012年第5期847-855,共9页 中国高等学校学术文摘·数学(英文)
关键词 Possibly non-unital function system operator system possibly non-unital operator system Possibly non-unital function system, operator system, possibly non-unital operator system
  • 相关文献

参考文献7

  • 1Effros E G,Ruan Z-J. Operator Spaces[A].Oxford:Oxford University Press,2000.
  • 2Kavruk A S,Paulsen V I,Todorov I G,Tomforde A M. Tensor products of operator systems[J].Journal of Functional Analysis,2011.267-299.
  • 3Ng C K. Operator subspaces of L(H) with induced matrix orderings[J].Indiana University Mathematics Journal,.
  • 4Paulsen V I,Todorov I G,Tomforde A M. Operator system structures on ordered spaces[J].Proc Lond Math Soc (3),2011,(01):25-49.
  • 5Paulsen V I,Tomforde A M. Vector spaces with an order unit[J].Indiana University Mathematics Journal,2009.1319-1359.
  • 6Werner W. Subspaces of L(H) that are *-invariant[J].Journal of Functional Analysis,2002.207-223.
  • 7Werner W. Multipliers on matrix ordered operator spaces and some K-groups[J].Journal of Functional Analysis,2004,(2):356-378.doi:10.1016/j.jfa.2003.05.001.

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部