Weighted Moore-Penrose invertible and weighted EP Banach algebra elements
type: Item
instance of: scholarly article
zbMATH Open document ID: 1290.46037
DOI: 10.4134/JKMS.2013.50.6.1349
author: Enrico Boasso
author: Dragan S. Djordjević
author: Dijana Mosić
published in: Journal of the Korean Mathematical Society
publication date: 2013-12-17T00:00:00Z
full work available at URL: https://arxiv.org/abs/1401.0469
Mathematics Subject Classification ID: 46H05
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 47A05
zbMATH DE Number: 6239030
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: weighted Moore-Penrose inverse
zbMATH Keywords: EP element
zbMATH Keywords: weighted EP element
zbMATH Keywords: group inverse
MaRDI profile type: Publication
arXiv ID: 1401.0469
OpenAlex ID: W2963079170
title: Weighted Moore-Penrose invertible and weighted EP Banach algebra elements
review text: The paper under review is concerned with a thorough study of the so-called weighted Moore-Penrose invertible elements and the weighted EP elements of a unital complex Banach algebra \(A\). The case of operators on a Banach space is also considered. The authors call an element \(a\in A\) weighted Moore-Penrose invertible with respect to \(e\) and \(f\) (where \(e\) and \(f\) are positive invertible elements in \(A\)) if there exists (a necessarily unique) \(b\in A\) such that \(a=aba\), \(b=bab\), ab is a hermitian element of the algebra \(A\) equipped with the norm \(\| x\|_e=\| e^{1/2}xe^{-1/2}\|\), and \(ba\) is a hermitian element of \(A\) equipped with the norm \(\| x\|_f=\| f^{1/2}xf^{-1/2}\|\). Further, in the case where \(a\) and \(b\) commute, the authors say that \(a\) is a weighted EP element.
reviewed by: Armando R. Villena
description: scientific article; zbMATH DE number 6239030