Characterization of the matrix whose norm is determined by its action on decreasing sequences
نویسندگان
چکیده
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 the corresponding ones given by Bennett in Quart. J. Math. Oxford (2), 49(1998), 395-432, by Chen et al in J. Math. Anal. Appl. 273(2002), 160-171 and by Jameson in Illinois J. Math. 43(1999), 79-99.
منابع مشابه
Characterization of the matrix whose norm is determined by its action on decreasing sequences ( The exceptional cases )
Let A = (aj,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 nonnegative finite matrices.
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