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On Group Representations whose C ∗ ‐Algebra is an Ideal in its Von Neumann Algebra II
Author(s) -
Granirer Edmond E.
Publication year - 1982
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-26.2.308
Subject(s) - ideal (ethics) , algebra over a field , group (periodic table) , mathematics , library science , computer science , pure mathematics , physics , political science , law , quantum mechanics
. — Let T be a unitary continuous representation of the locally compact group G on the Hilbert space H^ and denote by L(H,)[LC(H^)] the algebra of all bounded [compact] linear operators on H^. T can be lifted in the usual way to a *-representation of L^G). Denote by C*(G) = C* the norm closure of rEL^G)] in L(H,) (with operator norm) and by VN,(G) = VN, the W*-algebra generated by ^L^G)] in L(H,). Let