## 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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