Non-linear triple product A*B - B*A derivations on *-algebras
Let 𝒜 be a unital prime *-algebra that possesses a nontrivial projection, and let Φ : 𝒜 → 𝒜 be a non-linear map which satisfies Φ(A ◇ B ◇ C) = Φ(A)◇ B ◇ C + A ◇ Φ(B) ◇ C + A ◇ B ◇ Φ(C) for all A, B, C∈𝒜, where A ◇ B = A*B - B*A. Then, if Φ(α I⁄2) is self-adjoint map for α∈ {1,i} we show...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2024-02-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | https://www.utgjiu.ro/math/sma/v19/p19_04.pdf |
| _version_ | 1797300172753993728 |
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| author | Mohammad Shavandi Ali Taghavi |
| author_facet | Mohammad Shavandi Ali Taghavi |
| author_sort | Mohammad Shavandi |
| collection | DOAJ |
| description | Let 𝒜 be a unital prime *-algebra that possesses a nontrivial projection, and let Φ : 𝒜 → 𝒜 be a non-linear map which satisfies
Φ(A ◇ B ◇ C) = Φ(A)◇ B ◇ C + A ◇ Φ(B) ◇ C + A ◇ B ◇ Φ(C)
for all A, B, C∈𝒜, where A ◇ B = A*B - B*A. Then, if Φ(α I⁄2) is self-adjoint map for α∈ {1,i} we show that Φ is additive *-derivation. |
| first_indexed | 2024-03-07T23:02:26Z |
| format | Article |
| id | doaj.art-bc5f3e8b0b8a4d1087d26a3f88951587 |
| institution | Directory Open Access Journal |
| issn | 1843-7265 1842-6298 |
| language | English |
| last_indexed | 2024-03-07T23:02:26Z |
| publishDate | 2024-02-01 |
| publisher | University Constantin Brancusi of Targu-Jiu |
| record_format | Article |
| series | Surveys in Mathematics and its Applications |
| spelling | doaj.art-bc5f3e8b0b8a4d1087d26a3f889515872024-02-22T11:57:34ZengUniversity Constantin Brancusi of Targu-JiuSurveys in Mathematics and its Applications1843-72651842-62982024-02-0119 (2024)6778Non-linear triple product A*B - B*A derivations on *-algebrasMohammad Shavandi0Ali Taghavi 1University of Mazandaran, Faculty of Mathematical Sciences, Department of Mathematics, P. O. Box 47416-1468, Babolsar, Iran.Faculty of Mathematical Sciences, Department of Mathematics, P. O. Box 47416-1468, Babolsar, Iran. Let 𝒜 be a unital prime *-algebra that possesses a nontrivial projection, and let Φ : 𝒜 → 𝒜 be a non-linear map which satisfies Φ(A ◇ B ◇ C) = Φ(A)◇ B ◇ C + A ◇ Φ(B) ◇ C + A ◇ B ◇ Φ(C) for all A, B, C∈𝒜, where A ◇ B = A*B - B*A. Then, if Φ(α I⁄2) is self-adjoint map for α∈ {1,i} we show that Φ is additive *-derivation. https://www.utgjiu.ro/math/sma/v19/p19_04.pdfnew product derivationprime *-algebra; additive map |
| spellingShingle | Mohammad Shavandi Ali Taghavi Non-linear triple product A*B - B*A derivations on *-algebras Surveys in Mathematics and its Applications new product derivation prime *-algebra; additive map |
| title | Non-linear triple product A*B - B*A derivations on *-algebras |
| title_full | Non-linear triple product A*B - B*A derivations on *-algebras |
| title_fullStr | Non-linear triple product A*B - B*A derivations on *-algebras |
| title_full_unstemmed | Non-linear triple product A*B - B*A derivations on *-algebras |
| title_short | Non-linear triple product A*B - B*A derivations on *-algebras |
| title_sort | non linear triple product a b b a derivations on algebras |
| topic | new product derivation prime *-algebra; additive map |
| url | https://www.utgjiu.ro/math/sma/v19/p19_04.pdf |
| work_keys_str_mv | AT mohammadshavandi nonlineartripleproductabbaderivationsonalgebras AT alitaghavi nonlineartripleproductabbaderivationsonalgebras |