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

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

2007-09-29

arxiv.org/abs/0710.0038v1

Mathematics

Functional Analysis

Scientific paper

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.

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