# On the Space of Sequences of *p*-Bounded Variation and Related Matrix Mappings

## Authors

DOI: 10.1023/A:1025080820961

- Cite this article as:
- Başar, F. & Altay, B. Ukrainian Mathematical Journal (2003) 55: 136. doi:10.1023/A:1025080820961

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## 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} : ℓ_{1}), and the characterizations of some other matrix classes are obtained by means of a suitable relation.