A nonstandard proof of the spectral theorem for unbounded self-adjoint operators

TL;DR

This paper extends Moore's nonstandard proof of the spectral theorem from bounded to unbounded self-adjoint operators by utilizing Raab's nonstandard hull concept, broadening the theorem's applicability.

Contribution

It introduces a generalized nonstandard proof for unbounded self-adjoint operators, expanding the scope of spectral theorem proofs.

Findings

Successfully generalizes Moore's proof to unbounded operators

Uses Raab's nonstandard hull to handle unboundedness

Provides a new perspective on spectral theorem proofs

Abstract

We generalize Moore's nonstandard proof of the Spectral theorem for bounded self-adjoint operators to the case of unbounded operators. The key step is to use a definition of the nonstandard hull of an internally bounded self-adjoint operator due to Raab.