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Universal continuous calculus for Su*-algebras

par Schotz, Matthias
Référence Mathematische Nachrichten, 296, 6, page (2588-2608)
Publication Publié, 2023-06

Article révisé par les pairs

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Résumé :

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 (Figure presented.) -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.