On Orthogonal Projections of Symplectic Balls

Dias, C. Nuno; Gosson, A. Maurice; Prata, N. João

Publication

On Orthogonal Projections of Symplectic Balls

2024Review article

dc.contributor.author	Dias, C. Nuno
dc.contributor.author	Gosson, A. Maurice
dc.contributor.author	Prata, N. João
dc.date.accessioned	2025-11-11T10:47:51Z
dc.date.available	2025-11-11T10:47:51Z
dc.date.issued	2024
dc.description.abstract	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.	eng
dc.identifier.citation	Dias, N. C., de Gosson, M. A., & Prata, J. N. (2024). On orthogonal projections of symplectic balls. Comptes Rendus. Mathématique, 362(G3), 217-227.
dc.identifier.doi	10.5802/crmath.542
dc.identifier.uri	http://hdl.handle.net/10400.26/59608
dc.language.iso	eng
dc.peerreviewed	yes
dc.publisher	Académie des sciences
dc.relation.hasversion	https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.542/
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/
dc.subject	Symplectic ball
dc.subject	orthogonal projection
dc.subject	Gromov’s non-squeezing theorem
dc.title	On Orthogonal Projections of Symplectic Balls	eng
dc.title.alternative	Sur les projections orthogonales de boules symplectiques	eng
dc.type	review article
dspace.entity.type	Publication
oaire.citation.endPage	227
oaire.citation.startPage	217
oaire.citation.title	Comptes Rendus Mathématique
oaire.citation.volume	362
oaire.version	http://purl.org/coar/version/c_970fb48d4fbd8a85