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Abstract. In this paper we introduce a notion of $p$-classes in a proper $H^*$-algebra for which, in contrast with the definition due to Smith, an analogue of the duality of the $p$-classes of compact operators on a Hilbert space is valid. Furthermore, the cyclic and the irreducible $*$-representations of these classes and those of dual $B^*$-algebras are given.
AMS Subject Classification
(1991): 46K15, 47B10, 46K10
Keyword(s):
H^*,
-algebras,
centralizers,
spectral theorem of compact operators,
p,
-classes,
representations
Received March 20, 1992. (Registered under 5557/2009.)
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