The reverse order law \((ab)^\#=b^\dagger (a^\dagger abb^\dagger)^\dagger a^\dagger\) in rings with involution
type: Item
instance of: scholarly article
title: The reverse order law \((ab)^\#=b^\dagger (a^\dagger abb^\dagger)^\dagger a^\dagger\) in rings with involution
zbMATH Open document ID: 1331.15005
author: Dijana Mosić
author: Dragan S. Djordjević
published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
publication date: 2015-09-21T00:00:00Z
review text: For the reverse order law mentioned in the title and every of the laws \((ab)^\#=b^*(a^*abb^*)^\dagger a^*\), \((a^\dagger ab)^\#=b^\dagger(a^\dagger abb^\dagger)^\dagger\), \((abb^\dagger)^\#=(a^\dagger abb^\dagger)^\dagger a^\dagger\), \((a^*ab)^\#=b^*(a^*abb^*)^\dagger\) and \((abb^*)^\dagger = (a^*abb^*)^\dagger a^*\), the authors have found a group of equivalent conditions. Additionally, some sufficient conditions for the first two laws are given. Further, presented is a group of mutually equivalent (under a certain assumption) conditions which, in conjunction with the first of these laws, are necessary and sufficient for the identity \((ab)^\#=b^\dagger a^\dagger\) to hold.
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 16W10
zbMATH DE Number: 6483905
zbMATH Keywords: generalized inverse
zbMATH Keywords: group inverse
zbMATH Keywords: Moore-Penrose inverse
zbMATH Keywords: reverse order law
MaRDI profile type: Publication
full work available at URL: s13398-014-0178-2
OpenAlex ID: W2460236422
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DOI: 10.1007/S13398-014-0178-2
description: scientific article; zbMATH DE number 6483905