This is an announcement for the paper "Characterization of the matrix whose norm is determined by its action on decreasing sequences" by Chang-Pao Chen, Hao-Wei Huang, and Chun-Yen Shen. Abstract: Let $A=(a_{j,k})_{j,k \ge 1}$ be a non-negative matrix. In this paper, we characterize those $A$ for which $\|A\|_{E, F}$ are determined by their actions on decreasing sequences, where $E$ and $F$ are suitable normed Riesz spaces of sequences. Archive classification: math.FA Mathematics Subject Classification: 15A60, 40G05, 47A30, 47B37 The source file(s), HWHshenfinal.tex: 34262 bytes, is(are) stored in gzipped form as 0706.1098.gz with size 11kb. The corresponding postcript file has gzipped size 96kb. Submitted from: shenc@indiana.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0706.1098 or http://arXiv.org/abs/0706.1098 or by email in unzipped form by transmitting an empty message with subject line uget 0706.1098 or in gzipped form by using subject line get 0706.1098 to: math@arXiv.org.