On the Euler sequence spaces which include the spaces ℓ p and ℓ∞ I

Abstract: In the present paper, we introduce the Euler sequence space consisting of all sequences whose Euler transforms of order r are in the space ℓ p of non-absolute type which is the BK-space including the space ℓ p and prove that the spaces and ℓ p are linearly isomorphic for 1⩽ p ⩽∞. Furthermore, we give some inclusion relations concerning the space . Finally, we determine the α-, β- and γ-duals of the space for 1⩽ p ⩽∞ and construct the basis for the space , where 1⩽ p <∞. [Copyright &y& Elsevier]