  This paper deals with the problem of generalising Gromov's non squeezing
theorem to an infinite dimensional Hilbert phase space setting. By following
the lines of the proof by Hofer and Zehnder of finite dimensional
non-squeezing, we recover an infinite dimensional non-squeezing result by
Kuksin for symplectic diffeomorphisms which are non-linear compact
perturbations of a symplectic linear map. We also show that the infinite
dimensional non-squeezing problem, in full generality, can be reformulated as
the problem of finding a suitable Palais-Smale sequence for a distinguished
Hamiltonian action functional.
