A new perspective on paranormed Riesz sequence space of non-absolute type - Candan, Murat (Global Journal of Mathematical Analysis, 2015)
The current article mainly dwells on introducing Riesz sequence space \(r^{q}(\widetilde{B}_{u}^{p})\) which generalized the prior studies of Candan and Güneş [28], Candan and Kılınç [30] and consists of all sequences whose \(R_{u}^{q}\widetilde{B}\)-transforms are in the space \(\ell(p)\), where \(\widetilde{B}=B(r_{n},s_{n})\) stands for double sequential band matrix \((r_{n})^{∞}_{n=0}\) and \((s_{n})^{∞}_{n=0}\) are given convergent sequences of positive real numbers. Some topological properties of the new brand sequence space have been investigated as well as \(α\)- \(β\)-and \(γ\)-duals. Additionally, we have also constructed the basis of \(r^{q}(\widetilde{B}_{u}^{p})\). Eventually, we characterize a matrix class on the sequence space. These results are more general and more comprehensive than the corresponding results in the literature.