## Abstract

Let A = (a_{n, k})_{n, k ≥ 0} be a non-negative matrix. Denote by L_{p, q} (A) the supremum of those L satisfying {norm of matrix} AX {norm of matrix}_{q} ≥ L {norm of matrix} X {norm of matrix}_{p}(X ∈ ℓ_{p}, X ≥ 0), and define L_{(p), q} (A) = L_{p, q} (A)(p > 0) . We derive a range for the value of L_{p, q} (A_{W}^{NM}), where 0 < q ≤ p < 1 and A_{W}^{NM} denotes the Nörlund matrix associated with the weight function W. By the continuity of L_{(·), q} (A_{W}^{NM}), we show that this range is best possible. It is also proved that there exists a unique ξ ∈ (q, 1] such that L_{(·), q} (A_{W}^{NM}) maps [q, ξ] onto [1, {norm of matrix} W {norm of matrix}_{q} / {norm of matrix} W {norm of matrix}_{1}] and this mapping is continuous and strictly increasing. The case L_{p, q} ((A_{W}^{NM})^{t}) with - ∞ < p, q < 0 is also investigated.

Original language | English |
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Pages (from-to) | 1939-1948 |

Number of pages | 10 |

Journal | Linear Algebra and Its Applications |

Volume | 428 |

Issue number | 8-9 |

DOIs | |

State | Published - 15 Apr 2008 |

## Keywords

- Cesàro matrices
- Lower bound
- Nörlund matrices