Orlicz Spaces with Bicomplex Scalars

Abstract

In this paper we define bicomplex Orlicz space with hyperbolic valued Luxemburg norm and discussed some of their properties. We have also partially characterize an integral representation of a $\mathbb{D}$-valued convex function. Further we have shown that the spectrum of the unilateral shift operator on $l^2(\mathbb{BC})$ is the null cone $\mathcal{N}\mathcal{C}$.