Three-Point Trace Positivity:Schatten Norm Compression and Interpolating Metrics

Trung Dung Vuong, Hiroyuki Osaka

Let $(\mathcal{N},\nu )$ be a finite tracial von Neumann algebra and set ${\mathcal{K}}_r(P,Q)=\nu ((P^{1/2}Q{P}^{1/2}{)}^r)$. We prove that $$ [\mathcal{K}_r(P_i,P_j)]_{i,j=1}^3\ge0, \qquad 1/…