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Positive Schur properties in spaces of regular operators

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Abstract

Properties of Schur type for Banach lattices of regular operators and tensor products are analyzed. It is shown that the dual positive Schur property behaves well with respect to Fremlin’s projective tensor product, which allows us to construct new examples of spaces with this property. Similar results concerning the positive Grothendieck property are also presented.

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Acknowledgments

Most of the work on this paper was done during the author’s visit to the Adam Mickiewicz University. He wishes to thank the Department of Functional Analysis, and specially Professor W. Wnuk, for their great hospitality.

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Correspondence to Pedro Tradacete.

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This research has been supported by the Spanish Government through grants MTM2010-14946 and MTM2012-31286, as well as Grupo UCM 910346.

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Tradacete, P. Positive Schur properties in spaces of regular operators. Positivity 19, 305–316 (2015). https://doi.org/10.1007/s11117-014-0296-2

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