Henrik Wilming @arrr.de · Aug 7 Small paper w/ @lvanluijk.bsky.social and @stotti-alex.bsky.social: We revisit the amazing operator inequality by Lin et al. (arXiv:2211.13372), which implies strong sub-additivity of entropy and find that it's a special case of Connes' theory of spatial derivatives: arxiv.org/abs/2508.03731
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This clarifies the mathematical structure behind the inequality and immediately generalizes it to inclusions of arbitrary von Neumann algebras. The proof is essentially just as short as in the finite-dimensional case and boils down to APA* ≤ AA* for any projector P.