A note on families of generalized Nörlund matrices as bounded operators on lp

Proceedings of the Estonian Academy of Sciences

Ulrich Stadtmüller¹  Anne Tali¹ 

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关键词: operator theory;    Banach space lp;    bounded linear operators;    generalized Nörlund matrices;    Nörlund;    Riesz and Euler–Knopp matrices;   

DOI  :  10.3176/proc.2009.3.01

学科分类：化学（综合）

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

We deal with generalized Nörlund matrices A = (N, pn, qn) defined by means of two non-negative sequences (pn) and (qn) with p0, q0 > 0. We are interested in simple conditions such that the associated non-negative triangular matrix A = (ank) is a bounded linear operator on lp (1 < p < Â¥). Using results of D. Borwein (Canad. Math. Bull., 1998, 41, 10–14), we provide sufficient conditions and bounds for the norm ||A ||p. Our main question is whether certain families of generalized Nörlund matrices Aα = (N, pαn, qn) studied by different authors (see, e.g., Anal. Math., 2003, 29, 227–242; Math. Z., 1993, 214, 273–286) are bounded linear operators on lp. These matrices need not satisfy the sufficient conditions given by Borwein in the paper mentioned above. Explicit bounds for the norms ||Aα ||p are given.

【 授权许可】

Unknown