Let B(H) be the algebra of all bounded linear operators on a Hilbert space H. Automorphisms and antiautomorphisms are the only bijective linear mappings θ of B(H) with the property that θ(P) is an idempotent whenever P ∈ B(H) is. In case H is separable and infinite-dimensional, every local automorphism of B(H) is an automorphism.
@article{bwmeta1.element.bwnjournal-article-smv113i2p101bwm,
author = {Matej Bre\v sar and Peter \v Semrl},
title = {On local automorphisms and mappings that preserve idempotents},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {101-108},
zbl = {0835.47020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv113i2p101bwm}
}
Brešar, Matej; Šemrl, Peter. On local automorphisms and mappings that preserve idempotents. Studia Mathematica, Tome 113 (1995) pp. 101-108. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv113i2p101bwm/
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