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