  The global homeomorphism theorem for quasiconformal maps describes the
following specifically higher-dimensional phenomenon: {\em Locally invertible
quasiconformal mapping $f: {\R}^{n} \to {\R}^{n}$ is globally invertible
provided $n > 2$.}
  We prove the following operator version of the global homeomorphism theorem.
{\em If the operator $ f: H \to H $ acting in the Hilbert space $ H $ is
locally invertible and is an operator of bounded distortion, then it is
globally invertible.}
