Universal continuous calculus for Su*‐algebras

Matthias Schötz

Mathematische Nachrichten, 2023, vol. 296, issue 6, 2588-2608

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∗$C^*$‐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.

Date: 2023
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