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

2012/04/27 by Georgescu, Catalin, Picioroaga, Gabriel
#47A35 #47B47 #47C15 #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1204.6293

Abstract

We calculate the Fuglede-Kadison determinant for operators of the form ∑_i=1ⁿ M_fiL_gi where L_gi are unitaries or partial isometries coming from Borel (partial) isomorphisms g_i on a probability space which generate an ergodic equivalence relation, and M_fi 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.

Related

• Determinants on von Neumann algebras, Mahler measures and Ljapunov exponents
• The Fuglede-Kadison determinant, theme and variations
• Mahler measures and Fuglede--Kadison determinants
• Fuglede-Kadison determinants of matrix-valued semicircular elements and capacity estimates
• Applications of the Fuglede-Kadison determinant: Szegö's theorem and outers for noncommutative H^p