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

2007/09/29 by Chang-Pao Chen, Chen, Chang-Pao, Chun-Yen Shen +4
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #math.CA #math.FA #msc:15A60 #msc:47A30 #msc:47B37

paper · pdf · doi:10.48550/arxiv.0710.0038

arxiv created 2007/09/29 · arxiv updated 2009/12/01

Abstract

Let A=(a_j,k)_{j,k ≥ 1} be a non-negative matrix. In this paper, we characterize those A for which ‖A‖_ℓp,ℓq are determined by their actions on non-negative decreasing sequences, where one of p and q is 1 or ∞. The conditions forcing on A are sufficient and they are also necessary for non-negative finite matrices.

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