  Recently Kosaki proved an inequality for matrices that can be seen as a kind
of new uncertainty principle. Independently, the same result was proved by
Yanagi, Furuichi and Kuriyama. The new bound is given in terms of
Wigner-Yanase-Dyson informations. Kosaki himself asked if this inequality can
be proved in the setting of von Neumann algebras. In this paper we provide a
positive answer to that question and moreover we show how the inequality can be
generalized to an arbitrary operator monotone function.
