Positivity

, Volume 13, Issue 2, pp 435–441 | Cite as

The strong Schur property in Banach lattices

Article

Abstract

We prove that in the class of discrete Banach lattices the strong Schur property is equivalent to the disjoint strong Schur property (Theorem 3.1). Roughly speaking the strong Schur property holds iff an appropriate condition concerning sequences with positive pairwise disjoint terms is satisfied.

Keywords

Banach lattice Schur property strong Schur property subsequence splitting property 

Mathematics Subject Classification (2000)

46A40 46B42 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceA. Mickiewicz UniversityPoznańPoland

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