On the domain of q-Euler matrix in c and c0 with its point spectra

Abstract

We introduce new Banach spaces e?,? 0 (q) and e?,? c (q) defined as the domain of generalized q-Euler matrix E?,?(q) in the spaces c0 and c, respectively. Some topological properties and inclusion relations related to the newly defined spaces are exhibited. We determine the bases and obtain K?the duals of the spaces e?,? 0 (q) and e?,? c (q). We characterize certain matrix mappings from the spaces e?,? 0 (q) and e?,? c (q) to the space S ? {??, c, c0, ?1, bs, cs, cs0}. We compute necessary and sufficient conditions for a matrix operator to be compact from the space e?,? 0 (q) to the space S ? {??, c, c0, ?1, bs, cs, cs0} using Hausdorff measure of non-compactness. Finally, we give point spectrum of the matrix E?,?(q) in the space c.