(r<inf>1</inf>, r<inf>2</inf>) -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 V such that the class BVs of all bounded linear mappings between two arbitrary Banach spaces with the sequence of s-numbers in V constructs a map ideal. We define a new sequence space (cesr1,r2t)υ for definite functional υ by the domain of (r1, r2) -Cesàro matrix in ℓt, where r1, r2∈ (0 , ∞) and 1 ≤ t< ∞. We examine some geometric and topological properties of the multiplication mappings on (cesr1,r2t)υ and the pre-quasi ideal B(cesr1,r2t)υs.