An inequality related to uncertainty principle in von Neumann algebras

Details An inequality related to uncertainty principle in von Neumann algebras An inequality related to uncertainty principle in von Neumann algebras

2008-04-16

arxiv.org/abs/0804.2651v1

Physics

Mathematical Physics

accepted for publication in International Journal of Mathematics

Scientific paper

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.

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