On Orthogonal Projections of Symplectic Balls

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

http://hdl.handle.net/10400.26/59608

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Authors

Dias, C. Nuno

Gosson, A. Maurice

Prata, N. João

Abstract(s)

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.