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Universal continuous calculus for Su*‐algebras

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  • Matthias Schötz

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.

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  • Matthias Schötz, 2023. "Universal continuous calculus for Su*‐algebras," Mathematische Nachrichten, Wiley Blackwell, vol. 296(6), pages 2588-2608, June.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:6:p:2588-2608
    DOI: 10.1002/mana.202100136
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    1. Gennadiy Averkov, 2013. "Constructive Proofs of some Positivstellensätze for Compact Semialgebraic Subsets of ℝ d," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 410-418, August.
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