Bicomplex Sequence Spaces: Duality via Idempotent Decomposition

Abstract

This paper investigates the duals of some bicomplex sequence spaces corresponding to bicomplex functions that are holomorphic in the bicomplex space , or entire bicomplex sequence spaces. We investigate these spaces through their idempotent decompositions and examine the β-dual, γ-dual, and δ-dual. Precise definitions and analyses of these duals are presented.  Our results demonstrate that the duals of the original sequence spaces are strictly contained within the duals of their corresponding idempotent subclasses. These findings are also discussed in the context of algebra homomorphisms between the original sequence space  and its idempotent subclasses  and .