AI 中文总结
针对Tang和Zhang从公共左等角秩1族得到的c_p(m)闭式公式猜想，证明对所有m≥2及1<p<2均不成立，给出了相关Schatten范数不等式的反例。
AI 中文摘要
对于p≥1且m≥2，设c_p(m)为满足对所有复方阵都有‖∑_{k=1}^m A_k‖_p ≤ c_p(m)‖∑_{k=1}^m |A_k|‖_p的最小常数。Tang和Zhang近期从公共左等角秩1族得到c_p(m)的闭式公式猜想，我们对所有m≥2及1<p<2证明该公式不成立。
英文摘要
For $p\geq 1$ and $m\geq 2$, let $c_p(m)$ be the least constant such that \[ \left\|\sum_{k=1}^m A_k\right\|_p \leq c_p(m)\left\|\sum_{k=1}^m |A_k|\right\|_p \] for all square complex matrices. Tang and Zhang recently conjectured a closed formula for $c_p(m)$, obtained from a common-left equiangular rank-one family. We disprove that formula for every $m\geq2$ and every $1<p<2$.
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