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Matrices Whose Norms Are Determined by Their Actions on Decreasing Sequences

Published online by Cambridge University Press:  20 November 2018

Chang-Pao Chen
Affiliation:
Department of Applied Mathematics, Hsuan Chuang University, Hsinchu 300, Taiwan, Republic of China e-mail:, cpchen@wmail.hcu.edu.tw
Hao-Wei Huang
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, U.S.A. e-mail:, huang39@indiana.edue-mail:, shenc@indiana.edu
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Abstract

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Let $A={{({{a}_{j,k}})}_{j,k\ge 1}}$ be a non-negative matrix. In this paper, we characterize those $A$ for which ${{\left\| A \right\|}_{E,F}}$ are determined by their actions on decreasing sequences, where $E$ and $F$ are suitable normed Riesz spaces of sequences. In particular, our results can apply to the following spaces: ${{\ell }_{p}}$, $d(w,p)$, and ${{\ell }_{p}}(w)$. The results established here generalize ones given by Bennett; Chen, Luor, and Ou; Jameson; and Jameson and Lashkaripour.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2008

References

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