Title

Bounds For The Operator Norms Of Some Nörlund Matrices

Abstract

Suppose (pn)n≤o is a non-increasing sequence of non-negative numbers with p0 = 1, Pn = ∑j=0n pj, n = 0,1..., and A = A(pn) = (ank) is the lower triangular matrix defined by ank = Pn-k/Pn, 0 ≤ k ≤ n, and ank = 0, n < k. We show that the operator norm of A as a linear operator on ℓp is no greater than p/(p -1), for 1 < p < ∞; this generalizes, yet again, Hardy's inequality for sequences, and simplifies and improves, in this special case, more generally applicable results of D. Borwein, Cass, and Kratz. When the pn tend to a positive limit, the operator norm of A on ℓp is exactly p/(p-1). We also give some cases when the operator norm of A on ℓP is less than p/(p - 1). ©1996 American Mathematical Society.

Publication Date

12-1-1996

Publication Title

Proceedings of the American Mathematical Society

Volume

124

Issue

2

Number of Pages

543-547

Document Type

Article

Personal Identifier

scopus

Socpus ID

21344450316 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/21344450316

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