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A note on local automorphisms
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 981-986 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $H$ be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of $\mathcal B(H)$, the algebra of all bounded linear operators on a Hilbert space $H$, is an automorphism.
Let $H$ be an infinite-dimensional almost separable Hilbert space. We show that every local automorphism of $\mathcal B(H)$, the algebra of all bounded linear operators on a Hilbert space $H$, is an automorphism.
Classification : 46L40, 47B48
Keywords: automorphism; local automorphism; algebra of operators on a Hilbert space 
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     title = {A note on local automorphisms},
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     url = {http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a16/}
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Fošner, Ajda. A note on local automorphisms. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 981-986. http://geodesic.mathdoc.fr/item/CMJ_2006_56_3_a16/

[1] M.  Brešar, P.  Šemrl: On local automorphisms and mappings that preserve idempotents. Studia Math. 113 (1995), 101–108. | DOI | MR

[2] M.  Eidelheit: On isomorphisms of rings of linear operators. Studia Math. 9 (1940), 97–105. | DOI | MR | Zbl

[3] P. A.  Fillmore, W. E.  Longstaff: On isomorphisms of lattices of closed subspaces. Canad. J.  Math. 36 (1984), 820–829. | DOI | MR

[4] N.  Jacobson, C.  Rickart: Jordan homomorphisms of rings. Trans. Amer. Math. Soc. 69 (1950), 479–502. | DOI | MR

[5] D.  Larson, A. R.  Sourour: Local derivations and local automorphisms of  ${B}(X)$. Proc. Symp. Pure Math. 51 (1990), 187–194. | MR

[6] C.  Pearcy, D.  Topping: Sums of small numbers of idempotents. Michigan Math.  J. 14 (1967), 453–465. | DOI | MR