The Order Continuity of the Regular Norm on Regular Operator Spaces

The Order Continuity of the Regular Norm on Regular Operator Spaces

We present here some sufficient conditions for the regular norm on ℒr(E,F) to be order continuous, and for (ℒr(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 characteriz...

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Veröffentlicht in:Abstract and Applied Analysis 2013-01, Vol.2013 (2013), p.352-357-137
Hauptverfasser: Chen, Zi Li, Chen, Jin Xi, Feng, Ying
Format: Artikel
Sprache:eng
Schlagworte:
Continuity
Lattices
Norms
Operators
Studies
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Zusammenfassung:We present here some sufficient conditions for the regular norm on ℒr(E,F) to be order continuous, and for (ℒr(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 ℒr(E,F) is an Lp-space and is lattice isomorphic to an Lp-space for 1
ISSN:1085-3375
1687-0409
DOI:10.1155/2013/183786