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

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

2000-05-17

arxiv.org/abs/math/0005169v1

Mathematics

Operator Algebras

9 pages. To appear in Expo. Math

Scientific paper

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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