Matrices whose norms are determined by their actions on decreasing sequences
Journal
Canadian Journal of Mathematics
Journal Volume
60
Journal Issue
3
Pages
520-531
Date Issued
2008
Author(s)
Abstract
Abstract Let A = (aj,k) j,k≥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: ℓp , d(w, p) , and ℓp(w) . The results established here generalize ones given by Bennett; Chen, Luor, and Ou; Jameson; and Jameson and Lashkaripour.
Type
journal article