Local derivation on some class of subspace lattice algebras
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912179154845696 |
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| author | Chen, Hongjie Wang, Liguang Yang, Zhujun |
| author_facet | Chen, Hongjie Wang, Liguang Yang, Zhujun |
| contents | Let $\mathcal{H}$ be a separable Hilbert space and $\mathcal{L}_{0}\subset B(\mathcal{H})$ a complete reflexive lattice. Let $\mathscr{K}$ be the direct sum of $n_0$ copies of $\mathcal{H}$ ($n_{0}\in\mathbb{N}$ and $n_0\geq 2$) or the direct sum of countably infinite many copies of $\mathcal{H}$ respectively. We construct two class of subspace lattices $\mathcal{L}$ on $\mathscr{K}$. Let $Alg\mathcal{L}$ be the corresponding subspace lattice algebra. We show that every local derivation from $Alg\mathcal{L} $ into $B(\mathscr{K})$ is a derivation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02463 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local derivation on some class of subspace lattice algebras Chen, Hongjie Wang, Liguang Yang, Zhujun Operator Algebras Functional Analysis 47L75, 46L10 Let $\mathcal{H}$ be a separable Hilbert space and $\mathcal{L}_{0}\subset B(\mathcal{H})$ a complete reflexive lattice. Let $\mathscr{K}$ be the direct sum of $n_0$ copies of $\mathcal{H}$ ($n_{0}\in\mathbb{N}$ and $n_0\geq 2$) or the direct sum of countably infinite many copies of $\mathcal{H}$ respectively. We construct two class of subspace lattices $\mathcal{L}$ on $\mathscr{K}$. Let $Alg\mathcal{L}$ be the corresponding subspace lattice algebra. We show that every local derivation from $Alg\mathcal{L} $ into $B(\mathscr{K})$ is a derivation. |
| title | Local derivation on some class of subspace lattice algebras |
| topic | Operator Algebras Functional Analysis 47L75, 46L10 |
| url | https://arxiv.org/abs/2501.02463 |