Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces

We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see t...

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Autores principales: Sharma, Charu, Mohiuddine, Syed Abdul, Raj, Kuldip, Alkhaldi, Ali H.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5803401/
https://www.ncbi.nlm.nih.gov/pubmed/29456417
http://dx.doi.org/10.1186/s13660-018-1621-2
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author Sharma, Charu
Mohiuddine, Syed Abdul
Raj, Kuldip
Alkhaldi, Ali H.
author_facet Sharma, Charu
Mohiuddine, Syed Abdul
Raj, Kuldip
Alkhaldi, Ali H.
author_sort Sharma, Charu
collection PubMed
description We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see text] . We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequence dominates an Orlicz-Lorentz sequence. Finally, we study some geometric properties of these spaces and establish some inclusion relations between spaces.
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spelling pubmed-58034012018-02-14 Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces Sharma, Charu Mohiuddine, Syed Abdul Raj, Kuldip Alkhaldi, Ali H. J Inequal Appl Research We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see text] . We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequence dominates an Orlicz-Lorentz sequence. Finally, we study some geometric properties of these spaces and establish some inclusion relations between spaces. Springer International Publishing 2018-02-07 2018 /pmc/articles/PMC5803401/ /pubmed/29456417 http://dx.doi.org/10.1186/s13660-018-1621-2 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Sharma, Charu
Mohiuddine, Syed Abdul
Raj, Kuldip
Alkhaldi, Ali H.
Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces
title Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces
title_full Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces
title_fullStr Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces
title_full_unstemmed Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces
title_short Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces
title_sort orlicz-garling sequence spaces of difference operator and their domination in orlicz-lorentz spaces
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5803401/
https://www.ncbi.nlm.nih.gov/pubmed/29456417
http://dx.doi.org/10.1186/s13660-018-1621-2
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