Counterexamples to a conjectured Schatten norm inequality

Zhekai Pang

For $p\ge 1$ and $m\ge 2$, 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 comp…