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arXiv:0804.2651 · International Journal of Mathematics

AN INEQUALITY RELATED TO UNCERTAINTY PRINCIPLE IN VON NEUMANN ALGEBRAS

Paolo Gibilisco, Tommaso Isola

Published Nov 1, 2008• 2 citations
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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 et al. 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.

DOI
10.1142/s0129167x08005096

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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 et al. 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.