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.
2007
Bracci, Luciano; Picasso, LUIGI ETTORE
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/181322
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 9
social impact