On Absolute Tribonacci Series Spaces and Some Matrix Operators

Abstract

Recently, a number of studies related to the spaces of all sequences of summable by absolute summabilty methods and their matrix transformations have been presented by several authors. In this article, the absolute Tribonacci space $\left|T_\theta\right|_{q}$ is introduced as the domain of the Tribonacci matrix on $\ell_q$. First, certain algebraic and topological structure such as $BK-$space, isomorphism, duals and Schauder base are studied. Then, some characterizations of compact and matrix operators on this space are given, their norms and Hausdorff meausures of noncompactness are determined.