Matrices Whose Norms Are Determined by Their Actions on Decreasing Sequences

Abstract

Abstract. Let A = (a j,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: ℓ p , d (w, p), and ℓ p (w). The results established here generalize ones given

The bounds for matrices with monotonic rows

“…Corollary 3.6 and 4.6 give a partial answer to the Problem 7.23 in [1]. Moreover, Corollary 4.6 gives the part 0 < p ≤ 1, 0 < q < ∞ to · p, q which is determined by its actions on decreasing sequences, and this corollary complements the result for p, q ≥ 1 in [5] when X = p and Y = q . Corollaries 3.3 and 4.3 characterize the matrices A for which there exists x ∈ p such that L p , q (A) = Ax q or A p, q = Ax q .…”