On sequence spaces defined by the domain of a regular tribonacci matrix

Abstract

<jats:title>Abstract</jats:title><jats:p>In this article we introduce Tribonacci sequence spaces <jats:italic>ℓ<jats:sub>p</jats:sub></jats:italic>(<jats:italic>T</jats:italic>) (1 ≤ <jats:italic>p</jats:italic> ≤ ∞) derived by the domain of a newly defined regular Tribonacci matrix. We give some topological properties, inclusion relation, obtain the Schauder basis and determine the <jats:italic>α</jats:italic>-, <jats:italic>β</jats:italic>- and <jats:italic>γ</jats:italic>-duals of the new spaces. We characterize the matrix classes on <jats:italic>ℓ<jats:sub>p</jats:sub></jats:italic>(<jats:italic>T</jats:italic>). Finally, we give some geometric properties of the space <jats:italic>ℓ<jats:sub>p</jats:sub></jats:italic>(<jats:italic>T</jats:italic>).</jats:p>

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