On Orthogonal Projections of Symplectic Balls
We study the orthogonal projections of symplectic balls in $\mathbb{R}^{2n}$ on complex subspaces. In particular we show that these projections are themselves symplectic balls under a certain complexity assumption. Our main result is a refinement of a recent very interesting result of Abbondandolo a...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-05-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.542/ |
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| author | Dias, Nuno C. de Gosson, Maurice A. Prata, João N. |
| author_facet | Dias, Nuno C. de Gosson, Maurice A. Prata, João N. |
| author_sort | Dias, Nuno C. |
| collection | DOAJ |
| description | We study the orthogonal projections of symplectic balls in $\mathbb{R}^{2n}$ on complex subspaces. In particular we show that these projections are themselves symplectic balls under a certain complexity assumption. Our main result is a refinement of a recent very interesting result of Abbondandolo and Matveyev extending the linear version of Gromov’s non-squeezing theorem. We use a conceptually simpler approach where the Schur complement of a matrix plays a central role. An application to the partial traces of density matrices is given. |
| format | Article |
| id | doaj-art-dcdecd3594f24b9ebea9e2b7413b90af |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-05-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-dcdecd3594f24b9ebea9e2b7413b90af2025-02-07T11:19:53ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-05-01362G321722710.5802/crmath.54210.5802/crmath.542On Orthogonal Projections of Symplectic BallsDias, Nuno C.0de Gosson, Maurice A.1Prata, João N.2Escola Superior Náutica Infante D. Henrique. Av. Eng. Bonneville Franco, 2770-058 Paço d’Arcos, Portugal; Grupo de Física Matemática, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, PortugalUniversity of Vienna, Faculty of Mathematics (NuHAG), Vienna, AustriaEscola Superior Náutica Infante D. Henrique. Av. Eng. Bonneville Franco, 2770-058 Paço d’Arcos, Portugal; Grupo de Física Matemática, Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, PortugalWe study the orthogonal projections of symplectic balls in $\mathbb{R}^{2n}$ on complex subspaces. In particular we show that these projections are themselves symplectic balls under a certain complexity assumption. Our main result is a refinement of a recent very interesting result of Abbondandolo and Matveyev extending the linear version of Gromov’s non-squeezing theorem. We use a conceptually simpler approach where the Schur complement of a matrix plays a central role. An application to the partial traces of density matrices is given.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.542/Symplectic ballorthogonal projectionGromov’s non-squeezing theorem |
| spellingShingle | Dias, Nuno C. de Gosson, Maurice A. Prata, João N. On Orthogonal Projections of Symplectic Balls Comptes Rendus. Mathématique Symplectic ball orthogonal projection Gromov’s non-squeezing theorem |
| title | On Orthogonal Projections of Symplectic Balls |
| title_full | On Orthogonal Projections of Symplectic Balls |
| title_fullStr | On Orthogonal Projections of Symplectic Balls |
| title_full_unstemmed | On Orthogonal Projections of Symplectic Balls |
| title_short | On Orthogonal Projections of Symplectic Balls |
| title_sort | on orthogonal projections of symplectic balls |
| topic | Symplectic ball orthogonal projection Gromov’s non-squeezing theorem |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.542/ |
| work_keys_str_mv | AT diasnunoc onorthogonalprojectionsofsymplecticballs AT degossonmauricea onorthogonalprojectionsofsymplecticballs AT pratajoaon onorthogonalprojectionsofsymplecticballs |