Matrix Transformation and Compactness on q -Catalan Sequence Spaces

This article intends to develop q-Catalan sequence spaces lp(C(q)) and l∞(C(q)) due to q-Catalan matrix C(q) in lp and l∞, respectively. Apart from obtaining some basic topological properties and Schauder basis, we compute α-, β-, and γ-duals of the spaces lp(C(q)) and l∞(C(q)). We state and prove a theorem that characterize certain matrix classes (X, Y), where X is either of the space lp(C(q)) or l∞(C(q)) and Y∈{l∞,c0,c,l1}. The final section is devoted to determination of certain conditions by which a matrix operator becomes compact.