Article

Positivity

, Volume 13, Issue 2, pp 435-441

The strong Schur property in Banach lattices

  • Witold WnukAffiliated withFaculty of Mathematics and Computer Science, A. Mickiewicz University Email author 

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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