# Universal Continuous Calculus for Su*-Algebras

## TL;DR

This paper extends the concept of continuous calculus from C*-algebras to a broader class of Su*-algebras, enabling functional calculus for unbounded elements without relying on representation theory.

## Contribution

It introduces the existence of universal continuous calculi for finite tuples of commuting Hermitian elements in Su*-algebras, generalizing known results for C*-algebras.

## Key findings

- Established universal continuous calculus for Su*-algebras
- Derived new results on *-algebras of continuous functions
- Provided an elementary approach avoiding representation theory

## Abstract

Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and uniformly complete), such a universal continuous calculus exists. This generalizes the continuous calculus for C*-algebras to a class of generally unbounded ordered *-algebras. On the way, some results about *-algebras of continuous functions on locally compact spaces are obtained. The approach used throughout is rather elementary and especially avoids any representation theory.