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arXiv · 1301.4706

On a conjecture of A. Bikchentaev

Fedor Sukochev
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Abstract

In \cite{bik1}, A. M. Bikchentaev conjectured that for positive $τ-$measurable operators $a$ and $b$ affiliated with an arbitrary semifinite von Neumann algebra $\mathcal M$, the operator $b^{1/2}ab^{1/2}$ is submajorized by the operator $ab$ in the sense of Hardy-Littlewood. We prove this conjecture in full generality and present a number of applications to fully symmetric operator ideals, Golden-Thompson inequality and (singular) traces.

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Fedor Sukochev. 2013-01-20. On a conjecture of A. Bikchentaev. https://arxiv.org/abs/1301.4706

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