The Order Properties of r–compact Operators on Banach Lattices

We present here that (E,F), the space of all r-compact operators from E into F, is a generalised sublattice of ^sup ^sup r^^(E,F) for arbitary Banach lattices E and F, and that the characterization of the regular norm on (E,F) is order continuous. Some conditions for (E,F) to be a KB-space or a band...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2007-03, Vol.23 (3), p.457-466
Main Authors: Chen, Zi Li, Wickstead, A W
Format: Article
Language:English
Subjects:
Banach spaces
Lattices
Norms
Operators
Studies
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Summary:We present here that (E,F), the space of all r-compact operators from E into F, is a generalised sublattice of ^sup ^sup r^^(E,F) for arbitary Banach lattices E and F, and that the characterization of the regular norm on (E,F) is order continuous. Some conditions for (E,F) to be a KB-space or a band in ^sup ^sup r^^(E,F) are also provided.[PUBLICATION ABSTRACT]
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-005-0783-2