Unbounded p-Convergence in Lattice-Normed Vector Lattices

Creative Commons License

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

Siberian Advances in Mathematics, cilt.29, sa.3, ss.164-182, 2019 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 3
  • Basım Tarihi: 2019
  • Doi Numarası: 10.3103/s1055134419030027
  • Dergi Adı: Siberian Advances in Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.164-182
  • Anahtar Kelimeler: lattice-normed vector lattice, mixed-normed space, un-convergence, uo-convergence, vector lattice
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

© 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.