[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2018.58.2.271

On Some Spaces Isomorphic to the Space of Absolutely q-summable Double Sequences

Capan, Husamettin (Graduate School of Natural and Applied Sciences, Istanbul University, Beyazit Campus)
Basar, Feyzi (Inonu University)

Publication Information

Kyungpook Mathematical Journal / v.58, no.2, 2018 , pp. 271-289 More about this Journal

Abstract

Let 0 < q < ${\infty}$ . In this study, we introduce the spaces ${\mathcal{BV}}_q$ and ${\mathcal{LS}}_q$ of q-bounded variation double sequences and q-summable double series as the domain of four-dimensional backward difference matrix ${\Delta}$ and summation matrix S in the space ${\mathcal{L}}_q$ of absolutely q-summable double sequences, respectively. Also, we determine their ${\alpha}$ - and ${\beta}-duals$ and give the characterizations of some classes of four-dimensional matrix transformations in the case 0 < q ${\leq}$ 1.

Keywords

summability theory; double sequence; difference sequence space; double series; alpha-dual; beta-dual; matrix domain of 4-dimensional matrices; matrix transformations;

Citations & Related Records

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