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

Catalin Georgescu; Gabriel Picioroaga

paper

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

arXiv:1204.6293

Abstract

We calculate the Fuglede-Kadison determinant for operators of the form $\sum_{i = 1}^{n} M_{f_{i}} L_{g_{i}}$ 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 $M_{f_{i}}$ 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.

arXiv commentTo appear in Proceedings of the AMS