On the Space of Sequences of p-Bounded Variation and Related Matrix Mappings - Altay, B.; Başar, F. (Ukrains’kyi Matematychnyi Zhurnal, 2003)
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.