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AW<sup>∗</sup>-algebras are QW<sup>∗</sup>-algebras
introduced a class of Z?*-algebras called QΐF*-algebras which includes the W*-algebras and which is included in the class of A FF*-algebras.In this paper it is shown that the QJ^-algebras are exactly the ^lT7*-algebras.We shall use Reid's notation (see [2]) without further explanation.THEOREM.Let A be an AW*-algebra