Please use this identifier to cite or link to this item: https://scholar.ptuk.edu.ps/handle/123456789/473
Title: Unbounded p-Convergence in Lattice-Normed Vector Lattices
Authors: MARABEH, MOHAMMAD A. A.
Keywords: Vector Lattice
Lattice-Normed Vector Lattice
up-Convergence
uo-Convergence
un-Convergence
uaw-Convergence
Mixed-Normed Space
Issue Date: 2017
Publisher: Middle East Technical University
Abstract: The main aim of this thesis is to generalize unbounded order convergence, unbounded norm convergence and unbounded absolute weak convergence to lattice-normed vector lattices (LNVLs). Therefore, we introduce the following notion: a net (x_α) in an LNVL (X; p;E) is said to be unbounded p-convergent to x ∈ X (shortly, x_α up-converges to x) if p(|x_α- x|^ u) o→ 0 in E for all u ∈ X+. Throughout this thesis, we study general properties of up-convergence. Besides, we introduce several notions in lattice-normed vector lattices which correspond to notions from vector and Banach lattice theory. Finally, we study briefly the mixed-normed spaces and use them for an investigation of up-null nets and up-null sequences in lattice-normed vector lattices.
URI: https://scholar.ptuk.edu.ps/handle/123456789/473
Appears in Collections:PH.D

Files in This Item:
File Description SizeFormat 
PhD Thesis.pdf546.26 kBAdobe PDFThumbnail
View/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.