The first Szegö limit theorem for non-selfadjoint operators in the Følner algebra - Böttcher, Albrecht; Otte, Peter (MATHEMATICA SCANDINAVICA, 2005)
We determine the first order asymptotics of the trace of f(P_nUP_n) and the determinant P_nUP_n for operators U belonging to the Følner algebra associated with the sequence {P_n} and satisfying an "index zero" condition. We present three different proofs of the main result in the case where U is a normal operator.