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 $\mathcal{NC}$.