Some inequalities related to Hadamard matrices
type: Item
instance of: scholarly article
title: Some inequalities related to Hadamard matrices
zbMATH Open document ID: 1032.46012
DOI: 10.1023/A:1014486302617
author: Vakhtang V. Kvaratskhelia
publication date: 2004-03-15T00:00:00Z
review text: The author defines a parameter \(\rho^{(n)}\) connected with an \(n\times n\) matrix \(A=(a_{ki})\) and a normalized basis \((\varphi_k)\) of a Banach space \(X\) by \[ \rho^{(n)} := \max_{1\leq m\leq 2^n} \Biggl\|\sum_{i=1}^{2^n} \sum_{k=1}^m a_{ki}\varphi_i\Biggr\|. \] Throughout it is assumed that \((\varphi_k)\) is subsymmetric with constant \(1\). The first part deals with the case where \(A\) is a Sylvester matrix. The main result gives an upper estimate for the parameter in terms of the expressions \(\|\sum_{k=1}^n\varphi_k\|\). As corollaries, several other estimates for \(\rho^{(n)}\) and similar parameters are obtained. The value of \(\rho^{(n)}\) for \(l_1\) is given. A general lower estimate is also presented. In a next part, the parameter is evaluated for general Hadamard matrices. Finally an isomorphic characterization of \(l_1\) in terms of the asymptotics of the defined parameters is given. All results are stated without proofs.
Mathematics Subject Classification ID: 46B03
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 46B15
zbMATH DE Number: 1930639
zbMATH Keywords: Hadamard matrix
zbMATH Keywords: Sylvester matrix
zbMATH Keywords: subsymmetric basis
MaRDI profile type: Publication
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 1930639