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- Title
Universal continuous calculus for Su*‐algebras.
- Authors
Schötz, Matthias
- 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.
- Subjects
CALCULUS; CALCULI; REPRESENTATION theory; CONTINUOUS functions; FUNCTION algebras; SPECTRAL theory
- Publication
Mathematische Nachrichten, 2023, Vol 296, Issue 6, p2588
- ISSN
0025-584X
- Publication type
Article
- DOI
10.1002/mana.202100136