$(r_{1},r_{2})$-Cesàro summable sequence space of non-absolute type and the involved pre-quasi ideal

Abstract We suggest a sufficient setting on any linear space of sequences $\mathcal{V}$ V such that the class $\mathbb{B}^{s}_{\mathcal{V}}$ BVs of all bounded linear mappings between two arbitrary Banach spaces with the sequence ofs-numbers in $\mathcal{V}$ V constructs a map ideal. We define a new sequence space $(\mathit{ces}_{r_{1},r_{2}}^{t} )_{\upsilon }$ (cesr1,r2t)υ for definite functionalυby the domain of $(r_{1},r_{2})$ (r1,r2) -Cesàro matrix in $\ell _{t}$ ℓt , where $r_{1},r_{2}\in (0,\infty )$ r1,r2∈(0,∞) and $1\leq t<\infty $ 1≤t<∞ . We examine some geometric and topological properties of the multiplication mappings on $(\mathit{ces}_{r_{1},r_{2}}^{t} )_{\upsilon }$ (cesr1,r2t)υ and the pre-quasi ideal $\mathbb{B}^{s}_{ (\mathit{ces}_{r_{1},r_{2}}^{t} )_{\upsilon }}$ B(cesr1,r2t)υs .