A method of direct integral decomposition for very general classes of unbounded closed operators is developed. This method is applied to the reduction theory of partial *-algebras and Op*-algebras. As a consequence, representations of partial *-algebras are decomposed into irreducible ones and some states are decomposed into extremal states.
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Françoise D. Mathot, Integral Decomposition of Partial *-Algebras of Closed Operators. Publ. Res. Inst. Math. Sci. 22 (1986), no. 4, pp. 689–724DOI 10.2977/PRIMS/1195177628