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

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 $c_0(T).$