\(p\)-adic matrix valued inequalities
The author defines the \(p\)-adic matrix absolute value \(\vert A\vert_p\) to be the diagonal matrix of powers of \(p\) corresponding to torsion numbers. He proves \[ \vert A+B\vert_p\leq \max (\vert A\vert_p + \vert B\vert_p) \leq U \vert A\vert_p U^*+V\vert B\vert_pV^* \] for permutation matrices \(U\), \(V\) and conjectures, giving a \(3\times 3\) proof which he feels works in general, for some unitary \(U\), \(V\), \[ \vert AB\vert_p\leq \tfrac12(U\vert A\vert_p \vert B\vert_p U^* + V \vert A\vert_p \vert B\vert_p V^*). \]
scientific article; zbMATH DE number 3922884
scientific article