Local automorphisms of the unitary group and the general linear group on a Hilbert space
Lajos Molnar, Peter Semrl
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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