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Unbounded p-Convergence in Lattice-Normed Vector Lattices

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Abstract

A net xα in a lattice-normed vector lattice (X, p, E) is unbounded p-convergent to x ∈ X if \(p\left({\left| {{x_\alpha} - x} \right| \wedge u} \right)\buildrel o \over \longrightarrow \) 0 for every u ∈ X+. This convergence has been investigated recently for (X, p, E) = (X, |·|, X) under the name of uo-convergence, for (X, p, E) = (X, ‖·‖, ℝ) under the name of un-convergence, and also for \(\left({X,\;p,\;{\mathbb{R}^{X^{\prime}}}} \right)\), where p(x)[f]:= |f|(|x|), under the name uaw-convergence. In this paper we study general properties of the unbounded p-convergence.

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Acknowledgments

The authors would like to thank Professor Alexander Gutman for careful reading the manuscript and providing many valuable suggestions and improvements.

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Authors and Affiliations

  1. Muş Alparslan University, Muş, 49250, Turkey

    A. Aydın

  2. Middle East Technical University, Ankara, 06800, Turkey

    E. Emelyanov

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

    E. Emelyanov

  4. Hacettepe University, Ankara, 06800, Turkey

    N. Erkurşun-Özcan

  5. Palestine Technical University-Kadoorie, Tulkarem, Palestine

    M. Marabeh

Authors
  1. A. Aydın
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  2. E. Emelyanov
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  3. N. Erkurşun-Özcan
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  4. M. Marabeh
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Corresponding authors

Correspondence to A. Aydın, E. Emelyanov, N. Erkurşun-Özcan or M. Marabeh.

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The text was submitted by the authors in English.

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Aydın, A., Emelyanov, E., Erkurşun-Özcan, N. et al. Unbounded p-Convergence in Lattice-Normed Vector Lattices. Sib. Adv. Math. 29, 164–182 (2019). https://doi.org/10.3103/S1055134419030027

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  • DOI: https://doi.org/10.3103/S1055134419030027

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