Local automorphisms of the unitary group and the general linear group on a Hilbert space
Operator Algebras
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0005169,
title = {Local automorphisms of the unitary group and the general linear group on a Hilbert space},
author = {Lajos Molnar and Peter Semrl},
journal= {arXiv preprint arXiv:math/0005169},
year = {2007}
}
Comments
9 pages. To appear in Expo. Math