| Title:
|
A note on local automorphisms (English) |
| Author:
|
Fošner, Ajda |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
3 |
| Year:
|
2006 |
| Pages:
|
981-986 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
automorphism |
| Keyword:
|
local automorphism |
| Keyword:
|
algebra of operators on a Hilbert space |
| MSC:
|
46L40 |
| MSC:
|
47B48 |
| idZBL:
|
Zbl 1164.47334 |
| idMR:
|
MR2261670 |
| . |
| Date available:
|
2009-09-24T11:40:27Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128123 |
| . |
| Reference:
|
[1] M. Brešar, P. Šemrl: On local automorphisms and mappings that preserve idempotents.Studia Math. 113 (1995), 101–108. MR 1318418, 10.4064/sm-113-2-101-108 |
| Reference:
|
[2] M. Eidelheit: On isomorphisms of rings of linear operators.Studia Math. 9 (1940), 97–105. Zbl 0061.25301, MR 0004725, 10.4064/sm-9-1-97-105 |
| Reference:
|
[3] P. A. Fillmore, W. E. Longstaff: On isomorphisms of lattices of closed subspaces.Canad. J. Math. 36 (1984), 820–829. MR 0762744, 10.4153/CJM-1984-048-x |
| Reference:
|
[4] N. Jacobson, C. Rickart: Jordan homomorphisms of rings.Trans. Amer. Math. Soc. 69 (1950), 479–502. MR 0038335, 10.1090/S0002-9947-1950-0038335-X |
| Reference:
|
[5] D. Larson, A. R. Sourour: Local derivations and local automorphisms of ${B}(X)$.Proc. Symp. Pure Math. 51 (1990), 187–194. MR 1077437 |
| Reference:
|
[6] C. Pearcy, D. Topping: Sums of small numbers of idempotents.Michigan Math. J. 14 (1967), 453–465. MR 0218922, 10.1307/mmj/1028999848 |
| . |
