Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
automorphism; local automorphism; algebra of operators on a Hilbert space
automorphism; local automorphism; algebra of operators on a Hilbert space
Summary:
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.
References:
[1] M. Brešar, P. Šemrl: On local automorphisms and mappings that preserve idempotents. Studia Math. 113 (1995), 101–108. DOI 10.4064/sm-113-2-101-108 | MR 1318418
[2] M. Eidelheit: On isomorphisms of rings of linear operators. Studia Math. 9 (1940), 97–105. DOI 10.4064/sm-9-1-97-105 | MR 0004725 | Zbl 0061.25301
[3] P. A. Fillmore, W. E. Longstaff: On isomorphisms of lattices of closed subspaces. Canad. J. Math. 36 (1984), 820–829. DOI 10.4153/CJM-1984-048-x | MR 0762744
[4] N. Jacobson, C. Rickart: Jordan homomorphisms of rings. Trans. Amer. Math. Soc. 69 (1950), 479–502. DOI 10.1090/S0002-9947-1950-0038335-X | MR 0038335
[5] D. Larson, A. R. Sourour: Local derivations and local automorphisms of ${B}(X)$. Proc. Symp. Pure Math. 51 (1990), 187–194. MR 1077437
[6] C. Pearcy, D. Topping: Sums of small numbers of idempotents. Michigan Math. J. 14 (1967), 453–465. DOI 10.1307/mmj/1028999848 | MR 0218922
Search
Partner of
