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

Bişgin, Mustafa Cemil

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, Tome 19 (2020), pp. 155-170.

Résumé

In this work, we construct the sequence spaces f(Q(r,s,t,u)), f_0(Q(r,s,t,u)) and f_s(Q(r,s,t,u)), where Q(r,s,t,u) is quadruple band matrix which generalizes the matrices Δ^3, B(r,s,t), Δ^2, B(r,s) and Δ, where Δ^3, B(r,s,t), Δ^2, 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, f_0 and f_s, respectively. Moreover, we give the Schauder basis and β-, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.

Détail

Keywords: matrix domain, Schauder basis, beta- and gamma-duals, Banach Limits, almost convergence and matrix classes

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