A Counterexample to the Tang Zhang Schatten Norm Conjecture and Sharp Positive Results

Zijian Zeng, Houde Liu, Kurunathan Ratnavelu

For $m\ge 2$, let $c_p(m)$ be the all-dimensional best constant in $${\Vert \sum _{k=1}^m{A}_k\Vert }_p\le c_p(m){\Vert \sum _{k=1}^m|A_k|\Vert }_p.$$ Tang and Zhang conjectur…