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Characterization of an \(H^*\)-algebra in terms of a trace. (English) Zbl 0996.46024

The author characterizes \(H^*\)-algebras in terms of the trace defined on a certain subset of the algebra. He shows that any Banach *-algebra with a partially defined trace, and some additional properties, is a proper \(H^*\)-algebra with respect to some scalar product whose corresponding norm is equivalent to the original norm.

MSC:

46K15 Hilbert algebras
46K10 Representations of topological algebras with involution
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