Korean J. Math.  Vol 29, No 1 (2021)  pp.25-40
DOI: https://doi.org/10.11568/kjm.2021.29.1.25

On sequence spaces defined by the domain of tribonacci matrix in $c_0$ and $c$

Taja Yaying, Merve Ilkhan Kara

Abstract


In this article we introduce tribonacci sequence spaces $c_0(T)$ and $c(T)$ derived by the domain of a newly defined regular tribonacci matrix $T.$ We give some topological properties, inclusion relations, obtain the Schauder basis and determine $\alpha-,$ $\beta-$ and $\gamma-$ duals of the spaces $c_0(T)$ and $c(T).$ We characterize certain matrix classes $(c_0(T), Y)$ and $(c(T),Y),$ where $Y$ is any of the spaces $c_0, c$ or $\ell_{\infty}.$ Finally, using Hausdorff measure of non-compactness we characterize certain class of compact operators on the space $c_0(T).$   


Keywords


Tribonacci sequence space; Schauder basis; $\alpha-,$ $\beta-,$ $\gamma-$ duals; Matrix Transformation; Hausdorff measure of non-compactness

Subject classification

46A45, 46B45, 47B37, 47B07

Sponsor(s)



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