On the Space of Sequences of <em class="a-plus-plus">p</em>-Bounded Variation and Related Matrix Mappings

Abstract

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.