On topological properties of spaces obtained by the double band matrix

Abstract

Let λ denote any one of the spaces ℓ∞ and ℓp and λ(Ť) be the domain of the band matrix Ť. We study ℓp(Ť) for 1 ≤ p ≤ ∞ and give some inclusions and its topological properties. Also, we define the alpha−, beta− and gamma− duals of the space ℓp(Ť). Finally, we give some matrix mappings.

Keywords

• sequence spaces
• matrix transformations
• α−, β− and γ− duals
• 46a45
• 40c05
• 11b39