Characterization of matrix classes associated with $p$-absolutely summable sequences of bi-complex numbers

Abstract

In this paper, we  have characterized the bi-complex matrix transformations  on $\ell_{p}(\mathbb{C}_{2})$ space. We provide the necessary and sufficient requirements for an infinite bi-complex matrix to belong to $B(\ell_{2}(\mathbb{C}_{2}),\ell_{2}(\mathbb{C}_{2}))$. Additionally, we study when an infinite bi-complex matrix transforms $\ell_{1}(\mathbb{C}_{2})$ into $\ell_{\infty}(\mathbb{C}_{2})$ and provide a counterexample for the converse statement. We also provide some non trivial examples to support our claims.