Universal continuous calculus for Su*-algebras |
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Authors: | Matthias Schötz |
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Institution: | Département de mathématiques, Université libre de Bruxelles, Bruxelles, Belgium |
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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 -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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Keywords: | *-algebra continuous calculus representation theorem spectral theory |
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