Publication
On Orthogonal Projections of Symplectic Balls
| Summary: | We study the orthogonal projections of symplectic balls in R2n 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 approachwhere the Schur complement of a matrix plays a central role. An application to the partial traces of density matrices is given. |
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| Main Authors: | Dias, C. Nuno |
| Other Authors: | Gosson, A. Maurice; Prata, N. João |
| Subject: | Symplectic ball orthogonal projection Gromov’s non-squeezing theorem |
| Year: | 2024 |
| Country: | Portugal |
| Document type: | review article |
| Access type: | open access |
| Associated institution: | Escola Superior Náutica Infante D. Henrique |
| Language: | English |
| Origin: | Escola Superior Náutica Infante D. Henrique |
| Summary: | We study the orthogonal projections of symplectic balls in R2n 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 approachwhere the Schur complement of a matrix plays a central role. An application to the partial traces of density matrices is given. |
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