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For a trace τ on a semifinite von Neumann algebra we will prove τ((b 1/2 ab 1/2 ) rp )≤τ((b r/2 a r b r/2 ) p ). Here, r≥1, p>0, and a, b are positive operators

An inequality of Araki-Lieb-Thirring (von Neumann algebra case)