On a norm compression inequality for 2×N partitioned block matrices Original Research Article

We conjecture the following so-called norm compression inequality for 2×N partitioned block matrices and the Schatten p-norms: for pgreater-or-equal, slanted2,imagewhile for 1less-than-or-equals, slantpless-than-or-equals, slant2 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 2×N blocks is essential, by exhibiting counterexamples in the case of 3×3 and larger partitionings.