Fuglede-Kadison determinants for operators in the von Neumann algebra of an equivalence relation

Abstract

Abstract. We calculate the Fuglede-Kadison determinant for operators of the form n i=1 M fi L gi where L gi are unitaries or partial isometries coming from Borel (partial) isomorphisms g i on a probability space which generate an ergodic equivalence relation, and M fi are multiplication operators. We obtain formulas for the cases when the relation is treeable or the f i 's and g i 's satisfy some restrictions.