Unbounded p-Convergence in Lattice-Normed Vector Lattices

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Aydın A., EMELYANOV E., Erkurşun-Özcan N., Marabeh M.

Siberian Advances in Mathematics, vol.29, no.3, pp.164-182, 2019 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 29 Issue: 3
  • Publication Date: 2019
  • Doi Number: 10.3103/s1055134419030027
  • Journal Name: Siberian Advances in Mathematics
  • Journal Indexes: Scopus
  • Page Numbers: pp.164-182
  • Keywords: lattice-normed vector lattice, mixed-normed space, un-convergence, uo-convergence, vector lattice
  • Middle East Technical University Affiliated: Yes

Abstract

© 2019, Allerton Press, Inc.A net xα in a lattice-normed vector lattice (X, p, E) is unbounded p-convergent to x ∈ X if p(| xα− x| ∧ u) → o 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 (X, p, ℝX ′) , where p(x)[f]:= |f|(|x|), under the name uaw-convergence. In this paper we study general properties of the unbounded p-convergence.