All spectral dominant norms are stable (Q795900)

A norm \(\|.\|\) on \(M_ n(C)\) (the set of complex \(n\times n\) matrices) is called stable if there is a constant \(K>0\) such that \(\| A^ m\| \leq K\| A\|^ m\) for every \(A\in M_ n(C)\) and \(m\in N\). Clearly, each stable norm dominates the spectral radius. The main result is the converse, which was conjectured by \textit{C. R. Johnson} [ibid. 28, 117-130 (1979; Zbl 0432.15016)]. In the last section of the paper some problems are posed.