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Bibounded uo-convergence and b-property in vector lattices

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Abstract

We define bidual bounded uo-convergence in vector lattices and investigate relations between this convergence and b-property. We prove that for a regular Riesz dual system \(\langle X,X^{\sim }\rangle \), X has b-property if and only if the order convergence in X agrees with the order convergence in \(X^{\sim \sim }\).

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Authors and Affiliations

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

    Safak Alpay & Eduard Emelyanov

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

    Eduard Emelyanov

  3. Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia, 362027

    Svetlana Gorokhova

Authors
  1. Safak Alpay
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  2. Eduard Emelyanov
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  3. Svetlana Gorokhova
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Correspondence to Eduard Emelyanov.

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Alpay, S., Emelyanov, E. & Gorokhova, S. Bibounded uo-convergence and b-property in vector lattices. Positivity 25, 1677–1684 (2021). https://doi.org/10.1007/s11117-021-00840-7

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  • DOI: https://doi.org/10.1007/s11117-021-00840-7

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