Mixing Douglas' and weak majorization and factorization theorems
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913577966764032 |
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| author | Lissy, Pierre |
| author_facet | Lissy, Pierre |
| contents | The Douglas' majorization and factorization theorem characterizes the inclusion of operator ranges in Hilbert spaces. Notably, it reinforces the well-established connections between the inclusion of kernels of operators in Hilbert spaces and the (inverse) inclusion of the closures of the ranges of their adjoints. This note aims to present a ''mixed'' version of these concepts for operators with a codomain in a product space. Additionally, an application in control theory of coupled systems of linear partial differential equations is presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09305 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mixing Douglas' and weak majorization and factorization theorems Lissy, Pierre Functional Analysis Optimization and Control The Douglas' majorization and factorization theorem characterizes the inclusion of operator ranges in Hilbert spaces. Notably, it reinforces the well-established connections between the inclusion of kernels of operators in Hilbert spaces and the (inverse) inclusion of the closures of the ranges of their adjoints. This note aims to present a ''mixed'' version of these concepts for operators with a codomain in a product space. Additionally, an application in control theory of coupled systems of linear partial differential equations is presented. |
| title | Mixing Douglas' and weak majorization and factorization theorems |
| topic | Functional Analysis Optimization and Control |
| url | https://arxiv.org/abs/2411.09305 |