On a norm compression inequality for partitioned block matrices

Abstract: We conjecture the following so-called norm compression inequality for partitioned block matrices and the Schatten p-norms: for ,while for the ordering of the inequality is reversed. This inequality includes Hanner’s inequality for matrices as a special case. We prove several special cases of this inequality and show that the partitioning in blocks is essential, by exhibiting counterexamples in the case of and larger partitionings. [Copyright &y& Elsevier]