On the abstract theorem of Picard
type: Item
instance of: scholarly article
title: On the abstract theorem of Picard
zbMATH Open document ID: 1092.46508
author: M. I. Karahanyan
published in: Lobachevskii Journal of Mathematics
publication date: 2005-11-09T00:00:00Z
full work available at URL: https://eudml.org/doc/231698
full work available at URL: 6.html
review text: The result named in the title states that if \(A\) is a complex unital Banach algebra, \(J\) a two-sided closed ideal and \(D:A\rightarrow A\) a continuous derivation, then for any \(a\in A\) with \(Da\not\in J\) we have \[ \bigcup\{V((\exp \lambda D_J)({\widetilde a})):\lambda\in {\mathbf C}\}={\mathbf C}. \] Here \(V\) denotes the numerical range, \(D_J\) is the induced derivation on \(A/J\) and \({\widetilde a}\) is the coset of \(a\) in \(A/J\). Other results, of a rather technical nature, are also obtained.
Mathematics Subject Classification ID: 46H99
Mathematics Subject Classification ID: 47A12
Mathematics Subject Classification ID: 46H10
zbMATH DE Number: 2227256
zbMATH Keywords: Banach algebra
zbMATH Keywords: numerical range
reviewed by: Wiesław Tadeusz Żelazko
MaRDI profile type: Publication
description: scientific article