A short nonstandard proof of the Spectral Theorem for unbounded self-adjoint operators

TL;DR

This paper presents a concise and elementary proof of the Spectral Theorem for unbounded self-adjoint operators using nonstandard analysis, simplifying the traditional complex proof.

Contribution

It introduces a novel nonstandard analysis approach to prove the Spectral Theorem more simply and efficiently.

Findings

Provides a shorter proof of the Spectral Theorem for unbounded self-adjoint operators.

Demonstrates the effectiveness of nonstandard analysis in operator theory.

Simplifies understanding of spectral properties of unbounded operators.

Abstract

By nonstandard analysis, a very short and elementary proof of the Spectral Theorem for unbounded self-adjoint operators is given.