Linear maps preserving ideals of $C^{*}$-algebras
HTML articles powered by AMS MathViewer
- by Sang Og Kim PDF
- Proc. Amer. Math. Soc. 129 (2001), 1665-1668 Request permission
Abstract:
We show that unital self-adjoint linear bijections of matrix algebras, type $II_{1}$ factors and abelian $C^{*}$-algebras preserving maximal left ideals are isomorphisms and we show that a unital continuous linear map of a $C^{*}$-algebra $A$ that maps the minimal left ideal $Ap$ into itself is the identity map.References
- M. D. Choi, D. Hadwin, E. Nordgren, H. Radjavi, and P. Rosenthal, On positive linear maps preserving invertibility, J. Funct. Anal. 59 (1984), no. 3, 462–469. MR 769376, DOI 10.1016/0022-1236(84)90060-0
- B. E. Johnson, Centralisers and operators reduced by maximal ideals, J. London Math. Soc. 43 (1968), 231–233. MR 223890, DOI 10.1112/jlms/s1-43.1.231
- Lajos Molnár, Some linear preserver problems on $B(H)$ concerning rank and corank, Linear Algebra Appl. 286 (1999), no. 1-3, 311–321. MR 1661167, DOI 10.1016/S0024-3795(98)10189-1
- V. S. Shul′man, Operators preserving ideals in $C^*$-algebras, Studia Math. 109 (1994), no. 1, 67–72. MR 1267712, DOI 10.4064/sm-109-1-67-72
- Erling Størmer, On the Jordan structure of $C^{\ast }$-algebras, Trans. Amer. Math. Soc. 120 (1965), 438–447. MR 185463, DOI 10.1090/S0002-9947-1965-0185463-5
Additional Information
- Sang Og Kim
- Affiliation: Department of Mathematics, Hallym University, Chuncheon 200-702, Korea
- Email: sokim@sun.hallym.ac.kr
- Received by editor(s): August 31, 1999
- Published electronically: October 25, 2000
- Communicated by: Joseph A. Ball
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 1665-1668
- MSC (2000): Primary 47B49
- DOI: https://doi.org/10.1090/S0002-9939-00-06003-2
- MathSciNet review: 1814095