关于Bottcher-Wenzel不等式的注记
Remarks on the Bottcher-Wenzel Inequality
摘要：
在2005年，Böttcher和Wenzel提出了一个猜想：如果$X,Y$是实方阵，则有$||XY-YX||^2\leq 2||X||^2||Y||^2$，其中$||\cdot||$是Frobenius范数。在过去的几年里，几位作者发现了这个猜想的各种证明。我们在这里给出另一个证明。这个证明是高度概念化的，需要最少的计算。我们还简要讨论了相关的不等式，特别是经典的Chern-do Camo-Kobayashi不等式。
英文摘要：
In 2005, Böttcher and Wenzel raised the conjecture that if $X,Y$ are real square matrices, then $||XY-YX||^2\leq 2||X||^2||Y||^2$, where $||\cdot||$ is the Frobenius norm. Various proofs of this conjecture were found in the last few years by several authors. We here give another proof. This proof is highly conceptual and requires minimal computation. We also briefly discuss related inequalities, in particular, the classical Chern-do Camo-Kobayashi inequality.
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