The Frobenius norm and the commutator Original Research Article

In an earlier paper we conjectured an inequality for the Frobenius norm of the commutator of two matrices. This conjecture was recently proved by Seak-Weng Vong and Xiao-Qing Jin and independently also by Zhiqin Lu. We here give a completely different proof of this inequality, prove some related results, and embark on the corresponding question for unitarily invariant norms.