Komls properties in Banach lattices

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EMELYANOV E., ERKURŞUN ÖZCAN N., Gorokhova S. G.

ACTA MATHEMATICA HUNGARICA, vol.155, no.2, pp.324-331, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 155 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1007/s10474-018-0852-5
  • Journal Name: ACTA MATHEMATICA HUNGARICA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.324-331
  • Keywords: Banach lattice, o-convergence, uo-convergence, un-convergence, Komlos property, Komlos set, space of continuous functions
  • Middle East Technical University Affiliated: Yes

Abstract

Several Komls like properties in Banach lattices are investigated. We prove that C(K) fails the -pre-Komls property, assuming that the compact Hausdorff space K has a nonempty separable open subset U without isolated points such that every u U has countable neighborhood base. We prove also that, for any infinite dimension al Banach lattice E, there is an unbounded convex uo-pre-Komls set C which is not uo-Komls.