Work

Convergence of Spectral Truncations for Compact Metric Groups

Year: 2025

Type: article

Abstract: We study Gromov–Hausdorff convergence of state spaces for truncations of a compact metric group $G$ in momentum space. We work in the context of order-unit spaces and consider orthogonal projections $P_\Lambda $ in $L^{2}(G)$ corresponding to finite subsets of irreducible representations $\Lambda \subseteq \widehat G$ appearing in the Peter–Weyl decomposition of $G$. We then prove that the sequence of truncated state spaces $\{ S(P_\Lambda C(G) P_\Lambda )\}_\Lambda $ Gromov–Hausdorff converges to the original state space $S(C(G))$, when these are equipped with a metric associated to a Lip-norm which in turn is induced by the action of $G$.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf197

Authors: Yvann Gaudillot--Estrada, Walter D van Suijlekom

Institution: Radboud University Nijmegen

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,534

OpenAlex ID: W4411957319