<abstract xmlns="http://www.w3.org/1999/xhtml">In this work, we construct the sequence spaces <italic>f</italic>(<italic>Q</italic>(<italic>r, s, t, u</italic>)), <italic>f</italic>0(<italic>Q</italic>(<italic>r, s, t, u</italic>)) and <italic>fs</italic>(<italic>Q</italic>(<italic>r, s, t, u</italic>)), where <italic>Q</italic>(<italic>r, s, t, u</italic>) is quadruple band matrix which generalizes the matrices Δ3, <italic>B</italic>(<italic>r, s, t</italic>), Δ2, <italic>B</italic>(<italic>r, s</italic>) and Δ, where Δ3, <italic>B</italic>(<italic>r, s, t</italic>), Δ2, <italic>B</italic>(<italic>r, s</italic>) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are <italic>BK</italic>-spaces and are linearly isomorphic to the sequence spaces <italic>f</italic>, <italic>f</italic>0 and <italic>fs</italic>, respectively. Moreover, we give the Schauder basis and <italic>β</italic>, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.</abstract>

In this work, we construct the sequence spaces f(Q(r, s, t, u)), f0(Q(r, s, t, u)) and fs(Q(r, s, t, u)), where Q(r, s, t, u) is quadruple band matrix which generalizes the matrices Δ3, B(r, s, t), Δ2, B(r, s) and Δ, where Δ3, B(r, s, t), Δ2, B(r, s) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f0 and fs, respectively. Moreover, we give the Schauder basis and β, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.

Almost convergent sequence spaces derived by the domain of quadruple band matrix

Faculty Of Arts And Sciences, Department Of Mathematics

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

{"article-title":"Almost convergent sequence spaces derived by the domain of quadruple band matrix"}

In this work, we construct the sequence spaces f(Q(r, s, t, u)), f0(Q(r, s, t, u)) and fs(Q(r, s, t, u)), where Q(r, s, t, u) is quadruple band matrix which...

Almost convergent sequence spaces derived by the domain of quadruple band matrix

Published Online: Dec 31, 2020

Page range: 155 - 170

Received: Jul 17, 2019

Accepted: Apr 23, 2020

DOI: https://doi.org/10.2478/aupcsm-2020-0012

Keywords
matrix domain, Schauder basis, - and γ-duals, Banach Limits, almost convergence and matrix classes

© 2020 Mustafa Cemil Bişgin, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Almost convergent sequence spaces derived by the domain of quadruple band matrix

Published Online: Dec 31, 2020

Page range: 155 - 170

Received: Jul 17, 2019

Accepted: Apr 23, 2020

DOI: https://doi.org/10.2478/aupcsm-2020-0012

Keywordsmatrix domain, Schauder basis, - and γ-duals, Banach Limits, almost convergence and matrix classes

© 2020 Mustafa Cemil Bişgin, published by Sciendo

This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 International License.

Keywords
matrix domain, Schauder basis, - and γ-duals, Banach Limits, almost convergence and matrix classes