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 \(r^q(B_u^p)\) which generalized the prior studies of Candan and GÃ¼neÅŸ [28], Candan and KÄ±lÄ±nÃ§ [30] Â and consists of all sequences whose \(R_u^qB\)-transforms are in the space \((p)\), where \(B=B(r_n,s_n)\) 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 \(r^q(B_u^p)\). 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.