Brent Nelson

activity

20232026

collaborators

5 papers

math.OA2026

Irreducibility and weak spectral gap in free product von Neumann algebras

Aldo Garcia Guinto, Fehmi Ekin Giritlioglu, Rahul Kumar R. +2

Consider a free product $(M, φ) = (M_{1}, φ_{1}) * (M_{2}, φ_{2})$ of non-trivial von Neumann algebras. Using amalgamated free product techniques, we establish irreducibility and weak spectral…

math.OA2025

Almost unimodular groups

Aldo Garcia Guinto, Brent Nelson

We show that a locally compact group has open unimodular part if and only if the Plancherel weight on its group von Neumann algebra is almost periodic. We call such groups almost u…

math.OA2024

Uniqueness of extremal almost periodic states on the injective type III $_{1}$ factor

Michael Hartglass, Brent Nelson

Let $R_{\infty}$ denote the Araki--Woods factor -- the unique separable injective type III $_{1}$ factor. For extremal almost periodic states $φ, ψ \in (R_{\infty})_{*}$ , we show that if $…

math.OA2024

Murray-von Neumann dimension for strictly semifinite weights

Aldo Garcia Guinto, Matthew Lorentz, Brent Nelson

Given a von Neumann algebra $M$ equipped with a faithful normal strictly semifinite weight $φ$ , we develop a notion of Murray-von Neumann dimension over $(M, φ)$ that is defined for…

math.OA2023

Ergodic Quantum Processes on Finite von Neumann Algebras

Brent Nelson, Eric B. Roon

Let $(M, τ)$ be a tracial von Neumann algebra with a separable predual and let $(Ω, P)$ be a probability space. A bounded positive random linear operator on $L^{1} (M, τ)$ is a…

Irreducibility and weak spectral gap in free product von Neumann algebras

Almost unimodular groups

Uniqueness of extremal almost periodic states on the injective type III1​ factor

Murray-von Neumann dimension for strictly semifinite weights

Ergodic Quantum Processes on Finite von Neumann Algebras

Uniqueness of extremal almost periodic states on the injective type III $_{1}$ factor