Properties $\Gamma $ and $L$ for type ${\rm II}\sb{1}$\ factors

Paul Willig
1970 Proceedings of the American Mathematical Society  
Using the new concept of central sequences introduced by Dixmier and Lance, it is proved that for a type Hi factor on a separable Hilbert space properties T and L are equivalent. Let (J be a countably generated type IL factor. (The referee has pointed out that this is equivalent to the existence of a faithful scalar valued trace on a.) For AEQ-let ||.<4|| denote the operator bound of A and let |.4| = [tr(^4*^4)]1/2 where tr(A) is the normalized trace on
doi:10.1090/s0002-9939-1970-0259630-3 fatcat:muvtvtlj4jaofiwotl7nf6ue4m