Geodesic
On local automorphisms and mappings that preserve idempotents
Studia Mathematica, Tome 113 (1995) no. 2, pp. 101-108
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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. 
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Matej Brešar. On local automorphisms and mappings that preserve idempotents. Studia Mathematica, Tome 113 (1995) no. 2, pp. 101-108. doi: 10.4064/sm-113-2-101-108

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