This is an announcement for the paper "Characterization of the matrix whose norm is determined by its action on decreasing sequences: The exceptional cases" by Chang-Pao Chen, Chun-Yen Shen, and Kuo-Zhong Wang. Abstract: Let $A=(a_{j,k})_{j,k \ge 1}$ be a non-negative matrix. In this paper, we characterize those $A$ for which $\|A\|_{\ell_p,\ell_q}$ 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. Archive classification: math.FA math.CA Mathematics Subject Classification: 15A60, 47A30, 47B37 The source file(s), shenwang9409016.tex: 25759 bytes, is(are) stored in gzipped form as 0710.0038.gz with size 8kb. The corresponding postcript file has gzipped size 79kb. Submitted from: shenc@indiana.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0710.0038 or http://arXiv.org/abs/0710.0038 or by email in unzipped form by transmitting an empty message with subject line uget 0710.0038 or in gzipped form by using subject line get 0710.0038 to: math@arXiv.org.