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Abstract and Applied Analysis
Volume 2013, Article ID 183786, 6 pages
http://dx.doi.org/10.1155/2013/183786
Research Article

The Order Continuity of the Regular Norm on Regular Operator Spaces

School of Mathematics, Southwest Jiaotong University, Chengdu 610031, China

Received 28 March 2013; Accepted 24 May 2013

Academic Editor: Aref Jeribi

Copyright © 2013 Zi Li Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present here some sufficient conditions for the regular norm on to be order continuous, and for ( ) to be a KB-space. In particular we deduce a characterization of the order continuity of the regular norm using L- and M-weak compactness of regular operators. Also we characterize when the space is an -space and is lattice isomorphic to an -space for . Some related results are also obtained.