Bicomplex Linear Operators on Bicomplex Hilbert Spaces and Littlewood's Subordination Theorem

TL;DR

This paper explores properties of bicomplex linear operators on bicomplex Hilbert spaces, applies Hahn-Banach theorem in bicomplex Banach modules, and proves Littlewood's Subordination Theorem for bicomplex Hardy spaces.

Contribution

It introduces and analyzes bicomplex holomorphic function spaces and extends classical theorems to the bicomplex setting, providing new insights into bicomplex functional analysis.

Findings

Properties of bicomplex linear operators established

Hahn-Banach theorem applied to bicomplex Banach modules

Littlewood's Subordination Theorem proved for bicomplex Hardy space

Abstract

In this paper we study some basic properties of bicomplex linear operators on bicomplex Hilbert spaces. Further we discuss some applications of Hahn-Banach theorem on bicomplex Banach modules. We also introduce and discuss some bicomplex holomorphic function spaces and prove Littlewood's Subordination principle for bicomplex Hardy space.