Positivity

, Volume 13, Issue 2, pp 435–441

The strong Schur property in Banach lattices

Article

DOI: 10.1007/s11117-008-2252-5

Cite this article as:
Wnuk, W. Positivity (2009) 13: 435. doi:10.1007/s11117-008-2252-5

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 latticeSchur propertystrong Schur propertysubsequence splitting property

Mathematics Subject Classification (2000)

46A4046B42

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

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