New classes of double sequences in the domain of \({\mathcal {L}_p}\) and \({\mathcal {L}_\infty }\)

Abstract

The prime objective of this paper is to define new difference double sequence spaces in the domain of \(\mathcal {L}_p\) and \(\mathcal {L}_\infty\) via the double difference operator \(_2\Delta ^{\gamma , \mu }\) of orders \(\gamma , \mu\). The above spaces are normed linear spaces and they are linearly isomorphic to the spaces \({\mathcal {L}_p}\) and \({\mathcal {L}_\infty }\) for \(1\le p<\infty\). Also, some inclusion relations among them are derived.