Alternative-mean trace divergences: geometry, data processing, and barycenters

Trung Dung Vuong, Hiroki Shudo, Hiroyuki Osaka

Let $f:(0,\infty )\to (0,\infty )$ be a nontrivial normalized operator monotone function and set $s=f^{\prime }(1)$. We introduce the alternative-mean trace functional $$ \altPhi_f(A,B) :=\Tr(…