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The Order Properties of r–compact Operators on Banach Lattices

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Abstract

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

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Authors and Affiliations

  1. Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, P. R. China

    Zi Li Chen

  2. Department of Pure Mathematics, The Queen’s University of Belfast, Belfast BT7 1NN, Northern Ireland, UK

    A. W. Wickstead

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  1. Zi Li Chen
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  2. A. W. Wickstead
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Correspondence to Zi Li Chen.

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Chen, Z.L., Wickstead, A.W. The Order Properties of r–compact Operators on Banach Lattices. Acta Math Sinica 23, 457–466 (2007). https://doi.org/10.1007/s10114-005-0783-2

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  • DOI: https://doi.org/10.1007/s10114-005-0783-2

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