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

Mustafa Cemil Bişgin

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica (2020)

  • Volume: 19, page 155-170
  • ISSN: 2300-133X

Abstract

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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.

How to cite

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Mustafa Cemil Bişgin. "Almost convergent sequence spaces derived by the domain of quadruple band matrix." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 19 (2020): 155-170. <http://eudml.org/doc/296807>.

@article{MustafaCemilBişgin2020,
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.},
author = {Mustafa Cemil Bişgin},
journal = {Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica},
keywords = {matrix domain; Schauder basis; beta- and gamma-duals; Banach Limits; almost convergence and matrix classes},
language = {eng},
pages = {155-170},
title = {Almost convergent sequence spaces derived by the domain of quadruple band matrix},
url = {http://eudml.org/doc/296807},
volume = {19},
year = {2020},
}

TY - JOUR
AU - Mustafa Cemil Bişgin
TI - Almost convergent sequence spaces derived by the domain of quadruple band matrix
JO - Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
PY - 2020
VL - 19
SP - 155
EP - 170
AB - 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.
LA - eng
KW - matrix domain; Schauder basis; beta- and gamma-duals; Banach Limits; almost convergence and matrix classes
UR - http://eudml.org/doc/296807
ER -

References

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