Journal of Operator Theory

Volume 92, Issue 2, Autumn 2024 pp. 439-452.

On limit eigenvalue distributions associated to residual chains of groups

Authors: Jan Boschheidgen
Author institution: Departamento de Matematicas, Universidad Autonoma de Madrid, Madrid, 28049, Spain

Summary: Let $G$ be a residually finite group. We give an explicit example in the discrete Heisenberg group that the Brown measure of multiplication operators $A \in \mathbb{Z}[G] \subseteq \mathcal{B}(\ell^2(G))$ in general cannot be approximated using finite quotients $G/N$ of $G$ . We show that in finitely generated abelian groups the Brown measure can be approximated using finite quotients.

DOI: http://dx.doi.org/10.7900/jot.2022nov02.2406
Keywords: Brown measure, limit eigenvalue distribution, group algebra

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