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

Abstract

Let $A=(a_{j,k}{)}_{j,k\ge 1}$ be a non-negative matrix. In this paper, we characterize those $A$ for which $\Vert A{\Vert }_{E,F}$ are determined by their actions on decreasing sequences, where $E$ and $F$ are suitable normed Riesz spaces of sequences.

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