INTEGER OPERATORS IN FINITE VON NEUMANN ALGEBRAS

Motivated by the study of spectral properties of self-adjoint operators in the integral group ring of a sofic group, we define and study integer operators. We establish a relation with classical potential theory and in particular the circle of results obtained by Fekete and Szegö, see [3, 4, 13]. More concretely, we use results by Rumely, see [12], on equidistribution of algebraic integers to obtain a description of those integer operator which have spectrum of logarithmic capacity less than or equal to one. Finally, we relate the study of integer operators to a recent construction by Petracovici and Zaharescu, see [10].