Abstract and Applied Analysis

The Order Continuity of the Regular Norm on Regular Operator Spaces

Abstract

We present here some sufficient conditions for the regular norm on ${ℒ}^{r}\left(E,F\right)$ to be order continuous, and for (${ℒ}^{r}\left(E,F\right),\parallel ·{\parallel }_{r}$) 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 ${ℒ}^{r}\left(E,F\right)$ is an ${L}^{p}$-space and is lattice isomorphic to an ${L}^{p}$-space for $1. 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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