We present a new proof that the irreducible representations of the von Neumann algebra generated by a strongly continuous semigroup of partial isometries of index 1 are unique up to equivalence, as well as a proof that when such an algebra is a factor, its representations are completely reducible. As an application, we show that the irreducible representations of a strongly continuous semigroup of isometries {U(alpha), alpha >= 0} such that U(alpha)x [Graphics] 0 are equivalent.
Representations of semigroups of partial isometries
BRACCI, LUCIANO;PICASSO, LUIGI ETTORE
2007-01-01
Abstract
We present a new proof that the irreducible representations of the von Neumann algebra generated by a strongly continuous semigroup of partial isometries of index 1 are unique up to equivalence, as well as a proof that when such an algebra is a factor, its representations are completely reducible. As an application, we show that the irreducible representations of a strongly continuous semigroup of isometries {U(alpha), alpha >= 0} such that U(alpha)x [Graphics] 0 are equivalent.File in questo prodotto:
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