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

By Mohammad Mursaleen, Abdullah K. Noman. 2011

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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 < ∞.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7a90bcfc6a923bed4a8774074a1352cb30dbdd13