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


Authors: Catalin Georgescu and Gabriel Picioroaga
Journal: Proc. Amer. Math. Soc. 142 (2014), 173-180
MSC (2010): Primary 47C15, 47A35, 47B47
Published electronically: September 6, 2013
MathSciNet review: 3119192
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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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Additional Information

Catalin Georgescu
Affiliation: Department of Mathematical Sciences, The University of South Dakota, Dakota Hall, 414 East Clark Street, Vermillion, South Dakota 57069
Email: catalin.georgescu@usd.edu

Gabriel Picioroaga
Affiliation: Department of Mathematical Sciences, The University of South Dakota, Dakota Hall, 414 East Clark Street, Vermillion, South Dakota 57069
Email: gabriel.picioroaga@usd.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-11757-0
Keywords: Equivalence relation, von Neumann algebra, Fuglede-Kadison determinant
Received by editor(s): July 6, 2011
Received by editor(s) in revised form: February 22, 2012
Published electronically: September 6, 2013
Additional Notes: This research was partially supported by the Office of Research and the College of Arts and Sciences of the University of South Dakota under a 2011 Research Excellence Grant
Communicated by: Marius Junge
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.