On Maps that Preserve the Lie Products Equal to Fixed Elements
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911348050362368 |
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| author | Chaudhary, Shiv Kumar Prakash, Om |
| author_facet | Chaudhary, Shiv Kumar Prakash, Om |
| contents | This work characterizes the general form of a bijective linear map $Ψ:\mathscr{M}_n(\mathbb{C}) \to \mathscr{M}_n(\mathbb{C})$ such that $[Ψ(A_1),~Ψ(A_2)]=D_2$ whenever $[A_1,~A_2]=D_1$ where $D_1~\text{and}~D_2$ are fixed matrices. Additionally, let $\mathscr{H}_1$ and $\mathscr{H}_2$ be the infinite-dimensional complex Hilbert spaces. We characterize the bijective linear map $Ψ: \mathscr{B}(\mathscr{H}_1) \to \mathscr{B}(\mathscr{H}_2)$ where $Ψ(A_1) \circ ~Ψ(A_2)=D_2$ whenever $A_1\circ ~A_2=D_1$ and $D_1~\text{and}~D_2$ are fixed operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24912 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On Maps that Preserve the Lie Products Equal to Fixed Elements Chaudhary, Shiv Kumar Prakash, Om Rings and Algebras 15A04, 16W10 This work characterizes the general form of a bijective linear map $Ψ:\mathscr{M}_n(\mathbb{C}) \to \mathscr{M}_n(\mathbb{C})$ such that $[Ψ(A_1),~Ψ(A_2)]=D_2$ whenever $[A_1,~A_2]=D_1$ where $D_1~\text{and}~D_2$ are fixed matrices. Additionally, let $\mathscr{H}_1$ and $\mathscr{H}_2$ be the infinite-dimensional complex Hilbert spaces. We characterize the bijective linear map $Ψ: \mathscr{B}(\mathscr{H}_1) \to \mathscr{B}(\mathscr{H}_2)$ where $Ψ(A_1) \circ ~Ψ(A_2)=D_2$ whenever $A_1\circ ~A_2=D_1$ and $D_1~\text{and}~D_2$ are fixed operators. |
| title | On Maps that Preserve the Lie Products Equal to Fixed Elements |
| topic | Rings and Algebras 15A04, 16W10 |
| url | https://arxiv.org/abs/2512.24912 |