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.References
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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
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 173-180
- MSC (2010): Primary 47C15, 47A35, 47B47
- DOI: https://doi.org/10.1090/S0002-9939-2013-11757-0
- MathSciNet review: 3119192