A \(C^*\)-algebra on Schur algebras
type: Item
instance of: scholarly article
title: A \(C^*\)-algebra on Schur algebras
zbMATH Open document ID: 1213.46039
author: Pachara Chaisuriya
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2011-02-10T00:00:00Z
full work available at URL: https://eudml.org/doc/244402
full work available at URL: vol34 1 18.html
review text: For any \(\Lambda, \Sigma\in\{c_0\}\cup\{\ell_p\,|\,1\leq p<+\infty\}\), \(r\in\mathbb N\) and a Banach algebra \({\mathcal B}\), one has the Banach algebra \(S^r_{\Lambda,\Sigma}({\mathcal B})\) under the Schur product and the absolute Schur \(r\)-norm. In this paper, the author gives some relations between two different such algebras. In the case that \({\mathcal C}\) is a \(C^*\) algebra, it is shown that \(S^r_{\Lambda,\Sigma}({\mathcal C})\) becomes a \(C^*\) algebra under the induced involution operator if and only if \((\Lambda,\Sigma)=(\ell_1,c_0)\). A property of the relation of the absolute Schur \(r\)-norm and the Schur multiplier norm in \(S^r_{\Lambda,\Sigma}({\mathcal C})\) is also given.
reviewed by: Xiangqian Guo
Mathematics Subject Classification ID: 46H05
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 5849545
zbMATH Keywords: Banach algebra
zbMATH Keywords: C* algebra
zbMATH Keywords: Schur product
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5849545