Lower bounds on zero–one matrices

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

On Lower and Upper Bounds of Matrices

k=1 |ak|. Hardy’s inequality can be interpreted as the lp operator norm of the Cesàro matrix C, given by cj,k = 1/j, k ≤ j, and 0 otherwise, is bounded on lp and has norm ≤ p/(p − 1) (The norm is in fact p/(p − 1)). It is known that the Cesàro operator is not bounded below, or the converse of inequality (1.1) does not hold for any positive constant. However, if one assumes C acting only on non-...

Lower Bounds of Copson Type for Hausdorff Matrices on Weighted Sequence Spaces

Let = be a non-negative matrix. Denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. If we used instead of The purpose of this paper is to establish a Hardy type formula for , where is Hausdorff matrix and A similar result is also established for where In particular, we apply o...

Lower Bounds for Some Factorable Matrices

The following conjecture was posed by Axler and Shields. Let {xn} be a monotone decreasing sequence of nonnegative numbers, C the Cesáro matrix of order one. What is the best constant K for which ‖Cx‖2 ≥ K‖x‖2 for all such sequences {xn}? Lyons [3] determined that the best constant is π/ √ 6. This result was extended to p spaces for p > 1 by Bennett [1]. In [1], Bennett established the followin...

General Lower Bounds on Maximal Determinants of Binary Matrices

We prove general lower bounds on the maximal determinant of n× n {+1,−1}matrices, both with and without the assumption of the Hadamard conjecture. Our bounds improve on earlier results of de Launey and Levin (2010) and, for certain congruence classes of n mod 4, the results of Koukouvinos, Mitrouli and Seberry (2000). In an Appendix we give a new proof, using Jacobi’s determinant identity, of a...