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arXiv · 0804.2651

An inequality related to uncertainty principle in von Neumann algebras

Paolo Gibilisco·Tommaso Isola
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Abstract

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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Paolo Gibilisco, Tommaso Isola. 2008-04-16. An inequality related to uncertainty principle in von Neumann algebras. https://arxiv.org/abs/0804.2651

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