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

Mursaleen M. (Department of Mathematics, Aligarh Muslim University, Aligarh, India)
Noman Abdullah K. (Department of Mathematics, Aligarh Muslim University, Aligarh, India)

In the present paper, we introduce the sequence space lλp of non-absolute type and prove that the spaces ℓλp and lp are linearly isomorphic for 0 < p ≤ ∞. Further, we show that ℓλp 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 ℓλp. Finally, we construct the basis for the space ℓλp, where 1 ≤ p < ∞.

Keywords: Sequence space, BK-space, Schauder basis, Matrix mapping