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Matrices Whose Norms Are Determined by Their Actions on Decreasing Sequences

  Published:2008-06-01
 Printed: Jun 2008
  • Chang-Pao Chen
  • Hao-Wei Huang
  • Chun-Yen Shen
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Abstract

Let $A=(a_{j,k})_{j,k \ge 1}$ be a non-negative matrix. In this paper, we characterize those $A$ for which $\|A\|_{E, F}$ 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.
Keywords: norms of matrices, normed Riesz spaces, weighted mean matrices, Nörlund mean matrices, summability matrices, matrices with row decreasing norms of matrices, normed Riesz spaces, weighted mean matrices, Nörlund mean matrices, summability matrices, matrices with row decreasing
MSC Classifications: 15A60, 40G05, 47A30, 47B37, 46B42 show english descriptions Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]
Cesaro, Euler, Norlund and Hausdorff methods
Norms (inequalities, more than one norm, etc.)
Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
Banach lattices [See also 46A40, 46B40]
15A60 - Norms of matrices, numerical range, applications of functional analysis to matrix theory [See also 65F35, 65J05]
40G05 - Cesaro, Euler, Norlund and Hausdorff methods
47A30 - Norms (inequalities, more than one norm, etc.)
47B37 - Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
46B42 - Banach lattices [See also 46A40, 46B40]
 

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