Brent Nelson

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20232026

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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…

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

Murray-von Neumann dimension for strictly semifinite weights

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