Geodesic
The set of automorphisms of B(H) is topologically reflexive in B(B(H))
Studia Mathematica, Tome 122 (1997) no. 2, pp. 183-193
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The aim of this paper is to prove the statement announced in the title which can be reformulated in the following way. Let H be a separable infinite-dimensional Hilbert space and let Φ: B(H) → B(H) be a continuous linear mapping with the property that for every A ∈ B(H) there exists a sequence $(Φ_n)$ of automorphisms of B(H) (depending on A) such that $Φ(A)= lim_n Φ_n(A)$. Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).
DOI : 10.4064/sm-122-2-183-193
Keywords: reflexivity, automorphism, Jordan homomorphism, automatic surjectivity 
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Lajos Molnár. The set of automorphisms of B(H) is topologically reflexive in B(B(H)). Studia Mathematica, Tome 122 (1997) no. 2, pp. 183-193. doi: 10.4064/sm-122-2-183-193

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