The set of automorphisms of B(H) is topologically reflexive in B(B(H))
Molnár, Lajos
Studia Mathematica, Tome 122 (1997), p. 183-193 / Harvested from The Polish Digital Mathematics Library
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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 (Φn) of automorphisms of B(H) (depending on A) such that Φ(A)=limnΦn(A). Then Φ is an automorphism. Moreover, a similar statement holds for the set of all surjective isometries of B(H).

Publié le : 1997-01-01
EUDML-ID : urn:eudml:doc:216369 
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     volume = {122},
     year = {1997},
     pages = {183-193},
     zbl = {0871.47030},
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Molnár, Lajos. The set of automorphisms of B(H) is topologically reflexive in B(B(H)). Studia Mathematica, Tome 122 (1997) pp. 183-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv122i2p183bwm/

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