Characterization of the matrix whose norm is determined by its action on decreasing sequences:The exceptional cases

Abstract

Let $A=(a_{j,k}{)}_{j,k\ge 1}$ be a non-negative matrix. In this paper, we characterize those $A$ for which $\Vert A{\Vert }_{{\ell }_p,{\ell }_q}$ 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.

References in corpus (1)

• Characterization of the matrix whose norm is determined by its action on decreasing sequences

Cited by in corpus (1)

• On weighted mean matrices whose $l^p$ norms are determined on decreasing sequences