A study on q-analogue of Catalan sequence spaces


Taja Yaying, Merve Ìlkhan Kara, Bipan Hazarika, Emran Evren Kara




In this study, we construct q-analog C(q) of Catalan matrix and study the sequence spaces c 0 (C(q)) and c(C(q)) defined as the domain of q-Catalan matrix C(q) in the spaces c 0 and c, respectively. We exhibit some topological properties, obtain Schauder bases and determine α-, β-, and γ-duals of the spaces c 0 (C(q)) and c(C(q)). Finally, we characterize certain class of matrix mappings from the spaces c 0 (C(q)) and c(C(q)) to the space µ = {ℓ ∞ , c 0 , c, ℓ 1 } and give the necessary and sufficient conditions for a matrix operator to be compact.