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

Abstract

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

Keywords

• ( r 1 , r 2 ) $(r_{1},r_{2})$ -Cesàro matrix
• s-numbers
• Simple space
• Minimum space
• Multiplication map
• Pre-quasi ideal