Unbounded p-Convergence in Lattice-Normed Vector Lattices

A. Aydın; E. Emelyanov; N. Erkurşun-Özcan; M. Marabeh

doi:10.3103/S1055134419030027

Unbounded p-Convergence in Lattice-Normed Vector Lattices

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

Division of Analysis and Theory of Functions

Mus Alparslan University
Middle East Technical University
Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences
Palestine Technical University, Kadoorie

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

A net x_α in a lattice-normed vector lattice (X, p, E) is unbounded p-convergent to x ∈ X if p(| x_α− 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, ℝ^X ^′) , where p(x)[f]:= |f|(|x|), under the name uaw-convergence. In this paper we study general properties of the unbounded p-convergence.

Original language	English
Pages (from-to)	164-182
Number of pages	19
Journal	Siberian Advances in Mathematics
Volume	29
Issue number	3
DOIs	https://doi.org/10.3103/S1055134419030027
Publication status	Published - 1 Jul 2019

Keywords

lattice-normed vector lattice
mixed-normed space
un-convergence
uo-convergence
vector lattice

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10.3103/S1055134419030027

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title = "Unbounded p-Convergence in Lattice-Normed Vector Lattices",

abstract = "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.",

keywords = "lattice-normed vector lattice, mixed-normed space, un-convergence, uo-convergence, vector lattice",

author = "A. Aydın and E. Emelyanov and N. Erkur{\c s}un-{\"O}zcan and M. Marabeh",

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TY - JOUR

T1 - Unbounded p-Convergence in Lattice-Normed Vector Lattices

AU - Aydın, A.

AU - Emelyanov, E.

AU - Erkurşun-Özcan, N.

AU - Marabeh, M.

PY - 2019/7/1

Y1 - 2019/7/1

N2 - 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.

AB - 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.

KW - lattice-normed vector lattice

KW - mixed-normed space

KW - un-convergence

KW - uo-convergence

KW - vector lattice

UR - https://www.scopus.com/pages/publications/85071622536

U2 - 10.3103/S1055134419030027

DO - 10.3103/S1055134419030027

M3 - Article

AN - SCOPUS:85071622536

SN - 1055-1344

VL - 29

SP - 164

EP - 182

JO - Siberian Advances in Mathematics

JF - Siberian Advances in Mathematics

IS - 3

ER -

Unbounded p-Convergence in Lattice-Normed Vector Lattices

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Keywords

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