On $I$ and $I^*$-Cauchy conditions in $C^*$-algebra valued metric spaces

TL;DR

This paper explores $I$-Cauchy and $I^*$-Cauchy sequences in $C^*$-algebra valued metric spaces, extending the theory and introducing new concepts in this mathematical framework.

Contribution

It introduces and studies $I$-Cauchy and $I^*$-Cauchy sequences in $C^*$-algebra valued metric spaces, and proposes the concept of $C^*$-algebra valued normed spaces.

Findings

Properties of $I$-Cauchy sequences analyzed

Properties of $I^*$-Cauchy sequences analyzed

Introduction of $C^*$-algebra valued normed spaces

Abstract

The idea of $C^*$-algebra valued metric spaces was given by Z. Ma et al \cite{111} in 2014. Here we have studied the ideas of $I$-Cauchy and $I^*$-Cauchy sequences and their properties in such spaces and also we give the idea of $C^*$-algebra valued normed spaces.