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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| Дата: | 2021 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2021
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/188677 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-188677 |
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dspace |
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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 |
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