Some normed binomial difference sequence spaces related to the ℓ p $\ell_{p}$ spaces

Abstract

Abstract The aim of this paper is to introduce the normed binomial sequence spaces b p r , s ( ∇ ) $b^{r,s}_{p}(\nabla)$ by combining the binomial transformation and difference operator, where 1 ≤ p ≤ ∞ $1\leq p\leq\infty$ . We prove that these spaces are linearly isomorphic to the spaces ℓ p $\ell_{p}$ and ℓ ∞ $\ell _{\infty}$ , respectively. Furthermore, we compute Schauder bases and the α-, β- and γ-duals of these sequence spaces.

Keywords

• sequence space
• matrix domain
• Schauder basis
• α-, β- and γ-duals