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arXiv · 1911.03763

On Orthogonal Projections of Symplectic balls

Nuno Costa Dias·Maurice A. de Gosson·Joao Nuno Prata
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Abstract

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.

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BibTeXRIS

Nuno Costa Dias, Maurice A. de Gosson, Joao Nuno Prata. 2019-11-09. On Orthogonal Projections of Symplectic balls. https://doi.org/10.5802/crmath.542

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