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Domination properties and extension of positive compact operators on pre-Riesz spaces

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Abstract

This paper concerns the positive domination property of compact operators on pre-Riesz spaces. The method is embedding the pre-Riesz space into its Riesz completion. It also involves extension of order continuous norms. The compactness of the third power of a positive operator dominated by a compact operator is obtained in a pre-Riesz space which has an order unit.

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Acknowledgements

Feng Zhang is supported by a PhD scholarship of the China Scholarship Council. This paper was finished in Leiden University.

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Authors and Affiliations

  1. College of Mathematics, Taiyuan University of Technology, Taiyuan, 033000, People’s Republic of China

    Feng Zhang

  2. Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA, Leiden, The Netherlands

    Onno van Gaans

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  1. Feng Zhang
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  2. Onno van Gaans
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Correspondence to Feng Zhang.

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Zhang, F., van Gaans, O. Domination properties and extension of positive compact operators on pre-Riesz spaces. Rev Mat Complut 33, 89–101 (2020). https://doi.org/10.1007/s13163-019-00315-0

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  • DOI: https://doi.org/10.1007/s13163-019-00315-0

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