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Representations of semigroups of partial isometries
Author(s) -
Bracci L.,
Picasso L. E.
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdm059
Subject(s) - mathematics , pure mathematics
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 ( α ), α ⩾ 0} such that U ( α ) x → α → ∞ 0 are equivalent.