2016/05/02 by Dykema, K., Sukochev, F., Zanin, D. · 1 citation
#46L52 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1605.00349
Given a II1-factor M with tracial state τ and given an M-bimodule E(M,τ) of operators affiliated to M and a trace φ on E(M,τ), (namely, a linear functional that is invariant under unitary conjugation), we prove that detφ:Elog(M,τ)→[0,∞) defined by detφ(T)=exp(φ(log |T|)) is a multiplicative map on the set Elog(M,τ) of all affiliated operators T such that log+(|T|)\inE(M,τ). Finally, we show that all multiplicative maps on the invertible elements of Elog(M,τ) arise in this fashion.