Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
um-Topology in multi-normed vector lattices
Download
index.pdf
Date
2018-04-01
Author
Dabboorasad, Y. A.
Emelyanov, Eduard
Marabeh, M. A. A.
Metadata
Show full item record
This work is licensed under a
Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License
.
Item Usage Stats
109
views
0
downloads
Cite This
Let be a separating family of lattice seminorms on a vector lattice X, then is called a multi-normed vector lattice (or MNVL). We write if for all . A net in an MNVL is said to be unbounded m-convergent (or um-convergent) to x if for all . um-Convergence generalizes un-convergence (Deng et al. in Positivity 21:963-974, 2017; KandiAc et al. in J Math Anal Appl 451:259-279, 2017) and uaw-convergence (Zabeti in Positivity, 2017. doi:10.1007/s11117-017-0524-7), and specializes up-convergence (AydA +/- n et al. in Unbounded p-convergence in lattice-normed vector lattices. arXiv:1609.05301) and -convergence (Dabboorasad et al. in -Convergence in locally solid vector lattices. arXiv:1706.02006v3). um-Convergence is always topological, whose corresponding topology is called unbounded m-topology (or um-topology). We show that, for an m-complete metrizable MNVL , the um-topology is metrizable iff X has a countable topological orthogonal system. In terms of um-completeness, we present a characterization of MNVLs possessing both Lebesgue's and Levi's properties. Then, we characterize MNVLs possessing simultaneously the -Lebesgue and -Levi properties in terms of sequential um-completeness. Finally, we prove that every m-bounded and um-closed set is um-compact iff the space is atomic and has Lebesgue's and Levi's properties.
Subject Keywords
Vector lattice
,
Banach lattice
,
Multi-normed vector lattice
,
Um-Convergence
,
Um-Topology
,
Uo-Convergence
,
Un-Convergence
URI
https://hdl.handle.net/11511/48027
Journal
POSITIVITY
DOI
https://doi.org/10.1007/s11117-017-0533-6
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
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
Nonstandard hulls of lattice-normed ordered vector spaces
Aydin, Abdullah; Gorokhova, Svetlana; Gul, Hasan (2018-01-01)
Nonstandard hulls of a vector lattice were introduced and studied in many papers. Recently, these notions were extended to ordered vector spaces. In the present paper, following the construction of associated Banach-Kantorovich space due to Emelyanov, we describe and investigate the nonstandard hull of a lattice-normed space, which is the foregoing generalization of Luxemburg's nonstandard hull of a normed space.
Model-theory of vector-spaces over unspecified fields
Pierce, David (2009-06-01)
Vector spaces over unspecified fields can be axiomatized as one-sorted structures, namely, abelian groups with the relation of parallelism. Parallelism is binary linear dependence. When equipped with the n-ary relation of linear dependence for some positive integer n, a vector-space is existentially closed if and only if it is n-dimensional over an algebraically closed field. In the signature with an n-ary predicate for linear dependence for each positive integer n, the theory of infinite-dimensional vector...
Galois structure of modular forms of even weight
Gurel, E. (Elsevier BV, 2009-10-01)
We calculate the equivariant Euler characteristics of powers of the canonical sheaf on certain modular curves over Z which have a tame action of a finite abelian group. As a consequence, we obtain information on the Galois module structure of modular forms of even weight having Fourier coefficients in certain ideals of rings of cyclotomic algebraic integers. (c) 2009 Elsevier Inc. All rights reserved.
Tensor form factors of B -> K-1 transition from QCD light cone sum rules
Alıyev, Tahmasıb; Savcı, Mustafa (Elsevier BV, 2011-05-30)
The tensor form factors of B into p-wave axial vector meson transition are calculated within light cone QCD sum rules method. The parametrizations of the tensor form factors based on the series expansion are presented.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
Y. A. Dabboorasad, E. Emelyanov, and M. A. A. Marabeh, “um-Topology in multi-normed vector lattices,”
POSITIVITY
, pp. 653–667, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48027.