On some new sequence spaces of non-absolute type related to the spaces ℓp and ℓ∞ I

Abstract

In the present paper, we introduce the sequence space l?p of non-absolute type and prove that the spaces ??p and lp are linearly isomorphic for 0 < p ? ?. Further, we show that ??p is a p-normed space and a BK-space in the cases of 0 < p < 1 and 1 ? p ? ?, respectively. Furthermore, we derive some inclusion relations concerning the space ??p. Finally, we construct the basis for the space ??p, where 1 ? p < ?.