, Volume 55, Issue 1, pp 136-147

On the Space of Sequences of p -Bounded 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 BK-space 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 γ-duals 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 : ℓ1), and the characterizations of some other matrix classes are obtained by means of a suitable relation.