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

M. Mursaleen | Zendy; Abdullah K. Noman | Zendy

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

Author(s) -

M. Mursaleen,

Abdullah K. Noman

Publication year - 2011

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1102033m

Subject(s) - mathematics , space (punctuation) , sequence (biology) , type (biology) , normed vector space , basis (linear algebra) , sequence space , combinatorics , pure mathematics , banach space , geometry , ecology , philosophy , linguistics , biology , genetics

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 < ∞.

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