Review on Some Sequence Spaces of p-adic Numbers

Authors : Orhan Tuğ1 & Mutlay Doğan2
1&2Mathematics Education Department, Ishik University, Erbil, Iraq

Abstract:   In this paper, we make a literature review on p-adic sequences and we prove some new topological properties on the sequence spaces w(p), l(p) and c(p) of p-adic numbers as the set of all sequences, the set of bounded sequences and the set of convergent sequences of p-adic numbers, respectively. We show that these sequence spaces are Banach spaces under some certain topological properties. Moreover we prove some inclusion relation between these sequence spaces.We construct the α-, β- and γ duals of sequence spaces w(p), l(p) and c(p), and of p-adic numbers. We conclude the paper with characterizations of some significant matrix classes.

Keywords: Sequence Spaces, P-Adic Numbers, Banach Space, P-Adic Sequences, Matrix Transformations

doi: 10.23918/eajse.v3i1sip231

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