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1. Halmos and McLaughlin recently discovered [2 ] that a pair of arbitrary (bounded) operators on Hilbert space are unitarily equivalent if and only if a certain pair of associated partial isometries are also unitarily equivalent; thus they concluded that the unitary equivalence problem for the class of partial isometries is extremely difficult. The purpose of this present note is to show that partial isometries can be unpleasant in other ways. More specifically:

On certain von Neumann algebras which are generated by partial isometries