Norms of elementary operators
type: Item
instance of: scholarly article
zbMATH Open document ID: 0986.47029
author: Richard M. Timoney
publication date: 2002-01-02T00:00:00Z
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 46L05
zbMATH DE Number: 1684779
zbMATH Keywords: norm problem
zbMATH Keywords: elementary operator
zbMATH Keywords: Schauder basis
zbMATH Keywords: \(C^*\)-algebra
MaRDI profile type: Publication
title: Norms of elementary operators
published in: Irish Mathematical Society Bulletin
review text: Let \(E\) be a Banach space that contains an infinite dimensional complemented subspace with a Schauder basis, and \(A\) an algebra of bounded operators on \(E\) that contains the finite rank operators and endowed with the operator norm. For a given elementary operator \(Ta=\sum_{i=1}^\ell a_iab_i\in \mathcal{E}\ell\) on \(A\), a new one is defined by \(T^fa=\sum_{i=1}^\ell b_iaa_i\). The main result of the paper states that the map \(T\mapsto T^f\) is not continuous on \(\mathcal{E}\ell\), and it is claimed that this a variant of an unpublished result of Runde (to appear in J. Operator Th.), with an elementary proof. An editorial note says that an argument similar to the main theorem for the case of Hilbert space was provided by A. W. Wickstead.
reviewed by: Joan Cerdà
description: scientific article; zbMATH DE number 1684779