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

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