Banach triples with generalized inverses
type: Item
instance of: scholarly article
title: Banach triples with generalized inverses
zbMATH Open document ID: 0671.17003
DOI: 10.1007/BF01357724
author: Antonio Fernández López
author: E. García Rus
published in: Manuscripta Mathematica
publication date: 1988-01-01T00:00:00Z
review text: Penrose showed that for every complex rectangular matrix \(a\in M_{n\times m}({\mathbb{C}})\) there exists a unique \(b\in M_{n\times m}({\mathbb{C}})\), the generalized inverse of a, satisfying the following conditions: (i) \(aa^*b=a\), (ii) \(ba^*a=a\), (iii) \(bb^*a=b\), (iv) \(ab^*b=b\). These conditions can be expressed in terms of the triple product \(<abc>=ab^*c\) defined in \(A=M_{n\times m}({\mathbb{C}})\), \(b^*\) being the adjoint of b. With this triple product and with the operator norm, A is a complex Banach (associative) triple. In this note the authors determine all the complex Banach triples with generalized inverses.
Mathematics Subject Classification ID: 17A40
Mathematics Subject Classification ID: 46H70
Mathematics Subject Classification ID: 47L05
zbMATH DE Number: 4097587
zbMATH Keywords: complex Banach triples
zbMATH Keywords: generalized inverses
reviewed by: Sh. A. Ayupov
MaRDI profile type: Publication
cites work: Modulap annihilator jordan algebras
cites work: A ternary algebra with applications to matrices and linear transformations
cites work: Assoziative Tripelsysteme
cites work: Q5849795
full work available at URL: https://doi.org/10.1007/bf01357724
OpenAlex ID: W1971456973
description: scientific article; zbMATH DE number 4097587