Review on Some Sequence Spaces of p-adic Numbers

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