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

Georgescu, Catalin; Picioroaga, Gabriel

doi:10.1090/S0002-9939-2013-11757-0

Fuglede-Kadison determinants for operators in the von Neumann algebra of an equivalence relation
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by Catalin Georgescu and Gabriel Picioroaga PDF

Proc. Amer. Math. Soc. 142 (2014), 173-180 Request permission

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 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.

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