The purpose of this paper is to establish new log-majorization results concerning eigenvalues and singular values which generalize some previous work related to a conjecture and an open question which were presented by Lemos and Soares in 2018. In addition, we present a complement of a unitarily invariant norm inequality which was conjectured by Bhatia, Lim and Yamazaki in 2016, and recently proved by Dinh, Dumitru and Franco in 2017 for the Schatten p-norm with $1\le p\le \mathrm{\infty }$.

中文翻译：

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关于特征值和奇异值的新对数主要化结果以及范数不等式的补码

本文的目的是建立关于特征值和奇异值的新对数主要化结果，这些结果概括了 Lemos 和 Soares 在 2018 年提出的与猜想和开放问题相关的一些先前工作。此外，我们提出了一个补充单一不变范数不等式，由 Bhatia、Lim 和 Yamazaki 在 2016 年推测，最近由 Dinh、Dumitru 和 Franco 在 2017 年针对 Schatten p范数证明$\mathrm{1个}\le p\le \mathrm{\infty }$.