  Let $A=(a_{j,k})_{j,k \ge 1}$ be a non-negative matrix. In this paper, we
characterize those $A$ for which $\|A\|_{\ell_p,\ell_q}$ are determined by
their actions on non-negative decreasing sequences, where one of $p$ and $q$ is
1 or $\infty$. The conditions forcing on $A$ are sufficient and they are also
necessary for non-negative finite matrices.
