Bicomplex Riesz-Fischer Theorem

TL;DR

This paper extends the theory of bicomplex Hilbert spaces by establishing a bicomplex analogue of the Riesz-Fischer Theorem, demonstrating that the space l^2 serves as the canonical model in this context.

Contribution

It introduces a bicomplex version of the Riesz-Fischer Theorem, expanding the mathematical framework of bicomplex Hilbert spaces.

Findings

Established a bicomplex Riesz-Fischer Theorem

Proved that l^2 is the canonical model space in bicomplex Hilbert spaces

Derived a Best Approximation Theorem for bicomplex spaces

Abstract

This paper continues the study of infinite dimensional bicomplex Hilbert spaces introduced in previous articles on the topic. Besides obtaining a Best Approximation Theorem, the main purpose of this paper is to obtain a bicomplex analogue of the Riesz-Fischer Theorem. There are many statements of the Riesz-Fischer (R-F) Theorem in the literature, some are equivalent, some are consequences of the original versions. The one referred to in this paper is the R-F Theorem which establishes that the spaces $l^2$ is the canonical model space.