Abstract:
In this study, we construct the q-analog P(q) of Pascal matrix and study the sequence spaces c(P(q)) and c0(P(q)) defined as the domain of q-Pascal matrix P(q) in the spaces c and c0, respectively. We investigate certain topological properties, determine Schauder bases and compute Köthe duals of the spaces c0(P(q)) and c(P(q)). We state and prove the theorems characterizing the classes of matrix mappings from the space c(P(q)) to the spaces ∞ of bounded sequences and f of almost convergent sequences. Additionally, we also derive the characterizations of some classes of infinite matrices as a direct consequence of the results about the classes (c(P(q)), ℓ∞) and (c(P(q)), f)). Finally, we obtain the necessary and sufficient conditions for a matrix operator to be compact from the space c0(P(q)) to anyone of the spaces ℓ∞, c, c0, ℓ1, cs0, cs, bs. © 2022 A. Razmadze Mathematical Institute of Iv. Javakhishvili Tbilisi State University. All rights reserved.