Decomposition of Normal Operators and Its Application to Spectral Theorem

TL;DR

This paper extends a decomposition theorem from self-adjoint to normal operators, providing a new proof of the spectral theorem for unbounded normal operators, thereby advancing the theoretical understanding of operator spectral properties.

Contribution

It generalizes a known decomposition theorem to normal operators and offers a novel proof of the spectral theorem for unbounded cases.

Findings

Extended decomposition theorem to normal operators

Provided a new proof of the spectral theorem for unbounded normal operators

Enhanced theoretical framework for spectral analysis of operators

Abstract

A decomposition theorem for self-adjoint operators proved by Riesz and Lorch is extended to normal operators. This extension gives a new proof of the spectral theorem for unbounded normal operators.