Аннотация:http://arxiv.org/abs/2108.01408
Abstract. The global homeomorphism theorem for quasiconfor-
mal maps describes the following specifically higher-dimensional
phenomenon: Locally invertible quasiconformal mapping f : Rn →
Rn is globally invertible provided n > 2.
We prove the following operator version of the global homeo-
morphism theorem. If the operator f : H → H acting in the
Hilbert space H is locally invertible and is an operator of bounded
distortion, then it is globally invertible.