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Local automorphisms of the unitary group and the general linear group on a Hilbert space

Lajos Molnar·Peter Semrl
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Abstract

We prove that every 2-local automorphism of the unitary group or the general linear group on a complex infinite-dimensional separable Hilbert space is an automorphism. Thus these types of transformations are completely determined by their local actions on the two-points subsets of the groups in question.

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Lajos Molnar, Peter Semrl. 2000-05-17. Local automorphisms of the unitary group and the general linear group on a Hilbert space. https://arxiv.org/abs/math/0005169

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