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

Catalin Georgescu, Gabriel Picioroaga
2013 Proceedings of the American Mathematical Society  
We calculate the Fuglede-Kadison determinant for operators of the form n i=1 M f i L g i , where L g i are unitaries or partial isometries coming from Borel (partial) isomorphisms g i on a probability space which generate an ergodic equivalence relation and where M f i 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.
doi:10.1090/s0002-9939-2013-11757-0 fatcat:ilvfmbcotvgzxcm5zk6vfvdogm