Abstract and Applied Analysis

The Order Continuity of the Regular Norm on Regular Operator Spaces

Zi Li Chen, Ying Feng, and Jin Xi Chen

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Abstract

We present here some sufficient conditions for the regular norm on r ( E , F ) to be order continuous, and for ( r ( E , F ) , · r ) 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 r ( E , F ) is an L p -space and is lattice isomorphic to an L p -space for 1 < P < . Some related results are also obtained.

Article information

Source
Abstr. Appl. Anal., Volume 2013 (2013), Article ID 183786, 6 pages.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393511923

Digital Object Identifier
doi:10.1155/2013/183786

Mathematical Reviews number (MathSciNet)
MR3064541

Zentralblatt MATH identifier
1309.47046

Citation

Chen, Zi Li; Feng, Ying; Chen, Jin Xi. The Order Continuity of the Regular Norm on Regular Operator Spaces. Abstr. Appl. Anal. 2013 (2013), Article ID 183786, 6 pages. doi:10.1155/2013/183786. https://projecteuclid.org/euclid.aaa/1393511923


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