Representations of semigroups of partial isometries |
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Authors: | Bracci, L. Picasso, L. E. |
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Affiliation: | Dipartimento di Fisica Universitá di Pisa and Istituto Nazionale di Fisica Nucleare Sezione di Pisa Largo B. Pontecorvo 3 I - 56127 Pisa Italy luigi.picasso{at}df.unipi.it |
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Abstract: | 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. |
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