Positive Schur properties in spaces of regular operators
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.
KeywordsBanach lattice Positive Schur property Positive Grothendieck property Spaces of regular operators Fremlin tensor product
Mathematics Subject Classification (2010)46B42 46A32 47B65
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.
- 1.Aliprantis, C.D., Burkinshaw, O.: Positive Operators. Springer, New York (2006)Google Scholar
- 4.Diestel, J.: A survey of results related to the Dunford–Pettis property. In: Proceedings of the Conference on Integration, Topology, and Geometry in Linear Spaces (Univ. North Carolina, Chapel Hill, N.C., 1979), pp. 15–60, Contemp. Math., 2, Am. Math. Soc. (1980)Google Scholar
- 11.Meyer-Nieberg, P.: Banach Lattices. Springer, New York (1991)Google Scholar