Skip to main content
SpringerLink
Log in

Komlós properties in Banach lattices

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

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

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aliprantis C.D., Burkinshaw O.: Locally Solid Riesz Spaces with Applications to Economics, second ed.Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, (2003)

    Book  MATH  Google Scholar 

  2. Aliprantis C.D., Aliprantis C.D., Aliprantis C.D.: Positive Operators. Springer, Dordrecht (2006) reprint of the 1985 original.

    Book  MATH  Google Scholar 

  3. Deng Y., O’Brien M., Troitsky V.G.: Unbounded norm convergence in Banach lattices. Positivity, 21, 963–974 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gao N., Troitsky V.G., Xanthos F.: Uo-convergence and its applications to Cesàro means in Banach lattices. Israel J. Math. 220, 649–689 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  5. Kandić M., Marabeh M.A.A., Troitsky V.G.: Unbounded norm topology in Banach lattices. J. Math. Anal. Appl. 451, 259–279 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  6. Komlós J.: A generalization of a problem of Steinhaus, Acta Math. Acad. Sci. Hungar. 18, 217–229 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lennard C.: A converse to a theorem of Komlós for convex subsets of L 1, Pacific J.Math. 159, 75–85 (1993)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgement

The authors are grateful to the anonymous referee for helpful comments.

Author information

Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    E. Y. Emelyanov

  2. Department of Mathematics, Hacettepe University, 06800, Ankara, Turkey

    N. Erkurşun-Özcan

  3. Sobolev Institute of Mathematics, 630090, Novosibirsk, Russia

    E. Y. Emelyanov & S. G. Gorokhova

Authors
  1. E. Y. Emelyanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Erkurşun-Özcan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. G. Gorokhova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to N. Erkurşun-Özcan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Emelyanov, E.Y., Erkurşun-Özcan, N. & Gorokhova, S.G. Komlós properties in Banach lattices. Acta Math. Hungar. 155, 324–331 (2018). https://doi.org/10.1007/s10474-018-0852-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-018-0852-5

Key words and phrases

Mathematics Subject Classification

Search

Navigation