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LW-compact operators and domination problem

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Abstract

This paper introduces a ‘new’ class of operators. An operator T from a Banach lattice E into a Banach space Y will be called an LW-compact if T carries L-weakly compact sets of E into relatively compact sets of Y. Various characterizations of LW-compact operators are given. Also, we study the domination problem in this class of operators.

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Acknowledgements

The authors would like to express a profound gratitude to Professors Hamadi Baklouti and Karim Boulabiar.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Issat Kasserine, BP 471, Kasserine, 1200, Tunisia

    Mohamed Hajji

  2. Laboratoire de Recherche LATAO, Département de Mathematiques, Faculté des Sciences de Tunis, Université de Tunis El Manar, 2092, El Manar, Tunisia

    Mounir Mahfoudhi

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  1. Mohamed Hajji
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  2. Mounir Mahfoudhi
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Correspondence to Mounir Mahfoudhi.

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Hajji, M., Mahfoudhi, M. LW-compact operators and domination problem. Positivity 25, 1959–1972 (2021). https://doi.org/10.1007/s11117-021-00855-0

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  • DOI: https://doi.org/10.1007/s11117-021-00855-0

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