On Limit Eigenvalue Distributions Associated to Residual Chains of Groups

Jan Boschheidgen

On Limit Eigenvalue Distributions Associated to Residual Chains of Groups

Group Theory 2023-03-09 v3 Functional Analysis Operator Algebras

Authors: Jan Boschheidgen

Abstract

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 can not 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.

Keywords

residually finite group Brown measure limit eigenvalue distribution discrete Heisenberg group finite quotient group von Neumann algebra

Cite

@article{arxiv.2210.15240,
  title  = {On Limit Eigenvalue Distributions Associated to Residual Chains of Groups},
  author = {Jan Boschheidgen},
  journal= {arXiv preprint arXiv:2210.15240},
  year   = {2023}
}

Comments

Various Corrections,15 pages, 3 figures

On Limit Eigenvalue Distributions Associated to Residual Chains of Groups

Abstract

Keywords

Cite

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