On a generalization of decomposable maps on C*-algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918332400140288 |
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| author | Szczygielski, Krzysztof |
| author_facet | Szczygielski, Krzysztof |
| contents | We propose the notion of countable decomposability of maps on C*-algebras: a bounded linear map $φ: \mathscr{A}\to B(\mathcal{H})$, where $\mathscr{A}$ is a C*-algebra and $\mathcal{H}$ a Hilbert space, will be called countably decomposable if it admits a representation $φ= \sum_{k=1}^{\infty} ψ_k \circ ϕ_k$ for completely positive maps $ψ_k : \mathscr{A}\to B(\mathcal{H})$ and bounded *-maps $ϕ_k : \mathscr{A}\to\mathscr{A}$. A characterization of countable decomposability is given in certain cases with various assumptions imposed on maps $ϕ_k$. Our findings provide extensions of a classical result of Størmer from Proc. Amer. Math. Soc. 86 (1982), 402-404, originally formulated for decomposable positive maps. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_10753 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a generalization of decomposable maps on C*-algebras Szczygielski, Krzysztof Operator Algebras Mathematical Physics We propose the notion of countable decomposability of maps on C*-algebras: a bounded linear map $φ: \mathscr{A}\to B(\mathcal{H})$, where $\mathscr{A}$ is a C*-algebra and $\mathcal{H}$ a Hilbert space, will be called countably decomposable if it admits a representation $φ= \sum_{k=1}^{\infty} ψ_k \circ ϕ_k$ for completely positive maps $ψ_k : \mathscr{A}\to B(\mathcal{H})$ and bounded *-maps $ϕ_k : \mathscr{A}\to\mathscr{A}$. A characterization of countable decomposability is given in certain cases with various assumptions imposed on maps $ϕ_k$. Our findings provide extensions of a classical result of Størmer from Proc. Amer. Math. Soc. 86 (1982), 402-404, originally formulated for decomposable positive maps. |
| title | On a generalization of decomposable maps on C*-algebras |
| topic | Operator Algebras Mathematical Physics |
| url | https://arxiv.org/abs/2602.10753 |