Derivations of certain operator algebras
type: Item
instance of: scholarly article
title: Derivations of certain operator algebras
zbMATH Open document ID: 0968.47009
DOI: 10.1155/S0161171200003628
author: Jiankui Li
author: Hemant Pendharkar
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2000-11-20T00:00:00Z
full work available at URL: https://eudml.org/doc/48883
review text: Summary: Let \({\mathcal N}\) be a nest and let \({\mathcal A}\) be a subalgebra of \(L(H)\) all rank one operators of \(\text{alg }{\mathcal N}\). We give several conditions under which any derivation \(\delta\) from \({\mathcal A}\) into \(L(H)\) must be inner. The conditions include (1) \(H_-\neq H\), (2) \(0_+\neq 0\), (3) there is a nontrivial projection in \({\mathcal N}\) which is in \({\mathcal A}\), and (4) \(\delta\) is norm continuous. We also give some applications.
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 47L35
zbMATH DE Number: 1533314
zbMATH Keywords: nest algebra
zbMATH Keywords: triangular operator algebra
zbMATH Keywords: rank one operators
zbMATH Keywords: derivation
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1533314