Unbounded p-Convergence in Lattice-Normed Vector Lattices

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2019-07-01

Author

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

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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.

Subject Keywords

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

URI

https://hdl.handle.net/11511/94914

Journal

Siberian Advances in Mathematics

DOI

https://doi.org/10.3103/s1055134419030027

Collections

Department of Mathematics, Article

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Citation Formats

A. Aydın, E. Emelyanov, N. Erkurşun-Özcan, and M. Marabeh, “Unbounded p-Convergence in Lattice-Normed Vector Lattices,” Siberian Advances in Mathematics, vol. 29, no. 3, pp. 164–182, 2019, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/94914.