Representations of semigroups of partial isometries

We present a new proof that the irreducible representationsof the von Neumann algebra generated by a strongly continuoussemigroup of partial isometries of index 1 are unique up toequivalence, as well as a proof that when such an algebra isa factor, its representations are completely reducible. As anapplication, we show that the irreducible representations ofa strongly continuous semigroup of isometries {U(), 0} suchthat are equivalent.