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

  • B. Altay
  • F. Başar


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.
How to Cite
Altay, B., and F. Başar. “On the Space of Sequences of <em class="a-Plus-plus">p</Em&gt;-Bounded Variation and Related Matrix Mappings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 55, no. 1, Jan. 2003, pp. 108-1, https://umj.imath.kiev.ua/index.php/umj/article/view/3892.
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