On the Space of Sequences of pBounded Variation and Related Matrix Mappings
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The difference sequence spaces ℓ_{∞}(▵), c(▵), and c _{0}(▵) were studied by Kızmaz. The main purpose of the present paper is to introduce the space bv _{p} consisting of all sequences whose differences are in the space ℓ_{ p }, and to fill up the gap in the existing literature. Moreover, it is proved that the space bv _{p} is the BKspace including the space ℓ_{ p }. We also show that the spaces bv _{p} and ℓ_{ p } are linearly isomorphic for 1 ≤ p ≤ ∞. Furthermore, the basis and the α, β, and γduals of the space bv _{p} are determined and some inclusion relations are given. The last section of the paper is devoted to theorems on the characterization of the matrix classes (bv _{p} : ℓ_{∞}), (bv_{∞} : ℓ_{ p }), and (bv _{p} : ℓ_{1}), and the characterizations of some other matrix classes are obtained by means of a suitable relation.
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 Title
 On the Space of Sequences of pBounded Variation and Related Matrix Mappings
 Journal

Ukrainian Mathematical Journal
Volume 55, Issue 1 , pp 136147
 Cover Date
 20030101
 DOI
 10.1023/A:1025080820961
 Print ISSN
 00415995
 Online ISSN
 15739376
 Publisher
 Kluwer Academic PublishersPlenum Publishers
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