AbstractWe introduce an quantum entropy for bimodule quantum channels on finite von Neumann algebras, generalizing the remarkable Pimsner-Popa entropy. The relative entropy for Fourier multipliers of bimodule quantum channels establishes an upper bound of the quantum entropy. Additionally, we present the Araki relative entropy for bimodule quantum channels, revealing its equivalence to the rela...
Abstract：The Brascamp-Lieb inequalities are deep and beautiful inequalities on Euclidean spaces introduced by Brascamp and Lieb in 1976. They cover many fundamental and important inequalities such as Hölder's inequality, the Loomis-Whitney inequality, Young's inequality, etc. In this talk we give a short introduction to the Brascamp-Lieb inequalities and their applications. We prove one type o...
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