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Positivity

, Volume 19, Issue 2, pp 305–316 | Cite as

Positive Schur properties in spaces of regular operators

  • Pedro Tradacete
Article
  • 131 Downloads

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.

Keywords

Banach lattice Positive Schur property Positive Grothendieck property Spaces of regular operators Fremlin tensor product 

Mathematics Subject Classification (2010)

46B42 46A32 47B65 

Notes

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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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversidad Carlos III de MadridLeganés (Madrid)Spain

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