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

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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 : ℓ1), and the characterizations of some other matrix classes are obtained by means of a suitable relation.

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Authors and Affiliations

  1. Inönü Üniv., Turkey

    F. Başar & B. Altay

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  1. F. Başar
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  2. B. Altay
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Başar, F., Altay, B. On the Space of Sequences of p-Bounded Variation and Related Matrix Mappings. Ukrainian Mathematical Journal 55, 136–147 (2003). https://doi.org/10.1023/A:1025080820961

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