Krein-Šmul'jan Theorem Revisited
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866916859084800000 |
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| author | Zerbo, Santiago gonzalez Maestripieri, Alejandra Pería, Francisco Martínez |
| author_facet | Zerbo, Santiago gonzalez Maestripieri, Alejandra Pería, Francisco Martínez |
| contents | We present a generalization of Krein-Šmul'jan theorem which involves several operators. Given bounded selfadjoint operators $A,B_1,\ldots,B_m$ acting on a Hilbert space $\mathcal{H}$, we provide sufficient conditions to determine whether there are $λ_1,\ldots,λ_m\in \mathbb{R}$ such that $A + \sum_{i=1}^m λ_i B_i$ is a positive semidefinite operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_17525 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Krein-Šmul'jan Theorem Revisited Zerbo, Santiago gonzalez Maestripieri, Alejandra Pería, Francisco Martínez Functional Analysis 47A63, 47B02, 15A39, 90C20 We present a generalization of Krein-Šmul'jan theorem which involves several operators. Given bounded selfadjoint operators $A,B_1,\ldots,B_m$ acting on a Hilbert space $\mathcal{H}$, we provide sufficient conditions to determine whether there are $λ_1,\ldots,λ_m\in \mathbb{R}$ such that $A + \sum_{i=1}^m λ_i B_i$ is a positive semidefinite operator. |
| title | Krein-Šmul'jan Theorem Revisited |
| topic | Functional Analysis 47A63, 47B02, 15A39, 90C20 |
| url | https://arxiv.org/abs/2507.17525 |