Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators

In this paper, we study the reverse order law for the Moore–Penrose inverse of the product of three bounded linear operators in Hilbert spaces. We first present some equivalent conditions for the existence of the reverse order law ABC†=C†B†A†. Moreover, several equivalent statements of ℛAA∗ABC=ℛABC...

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Autores principales:	Yang Qi, Liu Xiaoji, Yu Yaoming
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/7ecd1b2a961b480db7420aa7604fc1aa
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spelling	oai:doaj.org-article:7ecd1b2a961b480db7420aa7604fc1aa2021-11-08T02:36:16ZDeveloping Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators2314-478510.1155/2021/6585951https://doaj.org/article/7ecd1b2a961b480db7420aa7604fc1aa2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/6585951https://doaj.org/toc/2314-4785In this paper, we study the reverse order law for the Moore–Penrose inverse of the product of three bounded linear operators in Hilbert spaces. We first present some equivalent conditions for the existence of the reverse order law ABC†=C†B†A†. Moreover, several equivalent statements of ℛAA∗ABC=ℛABC and ℛC∗CABC∗=ℛABC∗ are also deducted by the theory of operators.Yang QiLiu XiaojiYu YaomingHindawi LimitedarticleMathematicsQA1-939ENJournal of Mathematics, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Yang Qi Liu Xiaoji Yu Yaoming Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators
description	In this paper, we study the reverse order law for the Moore–Penrose inverse of the product of three bounded linear operators in Hilbert spaces. We first present some equivalent conditions for the existence of the reverse order law ABC†=C†B†A†. Moreover, several equivalent statements of ℛAA∗ABC=ℛABC and ℛC∗CABC∗=ℛABC∗ are also deducted by the theory of operators.
format	article
author	Yang Qi Liu Xiaoji Yu Yaoming
author_facet	Yang Qi Liu Xiaoji Yu Yaoming
author_sort	Yang Qi
title	Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators
title_short	Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators
title_full	Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators
title_fullStr	Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators
title_full_unstemmed	Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators
title_sort	developing reverse order law for the moore–penrose inverse with the product of three linear operators
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/7ecd1b2a961b480db7420aa7604fc1aa
work_keys_str_mv	AT yangqi developingreverseorderlawforthemoorepenroseinversewiththeproductofthreelinearoperators AT liuxiaoji developingreverseorderlawforthemoorepenroseinversewiththeproductofthreelinearoperators AT yuyaoming developingreverseorderlawforthemoorepenroseinversewiththeproductofthreelinearoperators
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Developing Reverse Order Law for the Moore–Penrose Inverse with the Product of Three Linear Operators

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