Representations of Hermitian Commutative *-Algebras by Unbounded Operators

TL;DR

This paper establishes a spectral theorem for unital representations of Hermitian commutative *-algebras by possibly unbounded operators, extending known results especially for countably generated algebras.

Contribution

It provides a spectral theorem for unital representations of Hermitian commutative *-algebras by unbounded operators, generalizing previous results for countably generated cases.

Findings

Spectral theorem for unital representations of Hermitian commutative *-algebras

Extension to possibly unbounded operators in pre-Hilbert spaces

Improved results for countably generated *-algebras

Abstract

We give a spectral theorem for unital representations of Hermitian commutative unital *-algebras by possibly unbounded operators in a pre-Hilbert space. A better result is known for the case in which the *-algebra is countably generated.