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Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras

Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras

In this paper, we proved that a bijective mapping Φ : A → B satisfies Φ(a ◦ b + baΦ) = Φ(a) ◦ Φ(b) + Φ(b)Φ(a)* (where ◦ is the special Jordan product on A and B, respectively), for all elements a, b ∈ A, if and only if Φ is a ∗-ring isomorphism. In particular, if the von Neumann algebras A and B are...

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Main Authors: Ferreira, J.C.M., Marietto, M.G.B.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2021
Series:Algebra and Discrete Mathematics
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/188677
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spelling irk-123456789-1886772023-03-12T01:28:59Z Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras Ferreira, J.C.M. Marietto, M.G.B. In this paper, we proved that a bijective mapping Φ : A → B satisfies Φ(a ◦ b + baΦ) = Φ(a) ◦ Φ(b) + Φ(b)Φ(a)* (where ◦ is the special Jordan product on A and B, respectively), for all elements a, b ∈ A, if and only if Φ is a ∗-ring isomorphism. In particular, if the von Neumann algebras A and B are type I factors, then Φ is a unitary isomorphism or a conjugate unitary isomorphism. 2021 Article Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras / J.C.M. Ferreira, M.G.B. Marietto // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 61–70. — Бібліогр.: 7 назв. — англ. 1726-3255 DOI:10.12958/adm1482 2020 MSC: 47B48, 46L10 http://dspace.nbuv.gov.ua/handle/123456789/188677 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description In this paper, we proved that a bijective mapping Φ : A → B satisfies Φ(a ◦ b + baΦ) = Φ(a) ◦ Φ(b) + Φ(b)Φ(a)* (where ◦ is the special Jordan product on A and B, respectively), for all elements a, b ∈ A, if and only if Φ is a ∗-ring isomorphism. In particular, if the von Neumann algebras A and B are type I factors, then Φ is a unitary isomorphism or a conjugate unitary isomorphism.
format Article
author Ferreira, J.C.M.
Marietto, M.G.B.
spellingShingle Ferreira, J.C.M.
Marietto, M.G.B.
Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras
Algebra and Discrete Mathematics
author_facet Ferreira, J.C.M.
Marietto, M.G.B.
author_sort Ferreira, J.C.M.
title Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras
title_short Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras
title_full Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras
title_fullStr Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras
title_full_unstemmed Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras
title_sort mappings preserving sum of products a ◦ b + ba* on factor von neumann algebras
publisher Інститут прикладної математики і механіки НАН України
publishDate 2021
url http://dspace.nbuv.gov.ua/handle/123456789/188677
citation_txt Mappings preserving sum of products a ◦ b + ba* on factor von Neumann algebras / J.C.M. Ferreira, M.G.B. Marietto // Algebra and Discrete Mathematics. — 2021. — Vol. 31, № 1. — С. 61–70. — Бібліогр.: 7 назв. — англ.
series Algebra and Discrete Mathematics
work_keys_str_mv AT ferreirajcm mappingspreservingsumofproductsabbaonfactorvonneumannalgebras
AT mariettomgb mappingspreservingsumofproductsabbaonfactorvonneumannalgebras
first_indexed 2023-10-18T23:08:54Z
last_indexed 2023-10-18T23:08:54Z
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