Unbounded p-convergence in lattice-normed vector lattices

Download

index.pdf

Date

2017

Author

Marabeh, Mohammad A. A.

Metadata

Show full item record

Item Usage Stats

273
views

138
downloads

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 follwing notion: a net $(x_alpha)$ in an LNVL $(X,p,E)$ is said to be unbounded $p$-convergent to $x in X$ (shortly, $x_alpha$ $up$- converges to $x$) if $p(lvert x_alpha −x rvert wedge u) xrightarrow{o}0$ 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.

Subject Keywords

Vector analysis., Lattice theory., Convergence.

URI

http://etd.lib.metu.edu.tr/upload/12620944/index.pdf
https://hdl.handle.net/11511/26426

Collections

Graduate School of Natural and Applied Sciences, Thesis

Suggestions

OpenMETU
Core

Bibounded uo-convergence and b-property in vector lattices Alpay, Safak; Emelyanov, Eduard; Gorokhova, Svetlana (2021-01-01) We define bidual bounded uo-convergence in vector lattices and investigate relations between this convergence and b-property. We prove that for a regular Riesz dual system ⟨ X, X∼⟩ , X has b-property if and only if the order convergence in X agrees with the order convergence in X∼ ∼.
Unbounded order convergence and the Gordon theorem# Gorokhova, S.G.; Kutateladze, S.S. (2019-01-01) The celebrated Gordon's theorem is a natural tool for dealing with universal completions of Archimedean vector lattices. Gordon's theorem allows us to clarify some recent results on unbounded order convergence. Applying the Gordon theorem, we demonstrate several facts on order convergence of sequences in Archimedean vector lattices. We present an elementary Boolean-Valued proof of the Gao-Grobler-Troitsky-Xanthos theorem saying that a sequence xn in an Archimedean vector lattice X is uo-null (uo-Cauchy) in ...
Unbounded p-Convergence in Lattice-Normed Vector Lattices Aydın, A.; Emelyanov, Eduard; Erkurşun-Özcan, N.; Marabeh, M. (2019-07-01) 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.
Vector and axial-vector couplings of D and D* mesons in 2+1 flavor lattice QCD Can, K. U.; ERKOL, GÜRAY; Oka, M.; Özpineci, Altuğ; Takahashi, T. T. (2013-02-12) Using the axial-vector coupling and the electromagnetic form factors of the D and D* mesons in 2 + 1 flavor lattice QCD, we compute the D*D pi, DD rho and D*D*rho coupling constants, which play an important role in describing the charm hadron interactions in terms of meson-exchange models. We also extract the charge radii of D and D* mesons and determine the contributions of the light and charm quarks separately.
uτ-Convergence in locally solid vector lattices Dabboorasad, Yousef A M; Emel’yanov, Eduard; Department of Mathematics (2018) We say that a net (xα) in a locally solid vector lattice (X,τ) is uτ-convergent to a vector x ∈ X if

Citation Formats

M. A. A. Marabeh, “Unbounded p-convergence in lattice-normed vector lattices,” Ph.D. - Doctoral Program, Middle East Technical University, 2017.