Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-13T05:45:42.650Z Has data issue: false hasContentIssue false
  • English
  • Français

Positive Linear Mappings Between C*-Algebras

Published online by Cambridge University Press:  20 November 2018

Yong Zhong
Yong Zhong*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 1A1, e-mail:zhong@math.toronto.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We prove that a positive unital linear mapping from a von Neumann algebra to a unital C*-algebra is a Jordan homomorphism if it maps invertible selfadjoint elements to invertible elements, and that for any compact Hausdorff space X, all positive unital linear mappings from C(X) into a unital C*-algebra that preserve the invertibility for self-adjoint elements are *-homomorphisms if and only if X is totally disconnected.

Keywords

46L0546J10C*-algebraJordan homomorphismtotally disconnected space
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 2 , 01 June 1995 , pp. 252 - 256
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Choi, Man-Duen, Hadwin, D., Nordgren, E., Radjavi, H. and Rosenthal, P., On positive linear maps preserving invertibility, J. Funct. Anal. 59(1984), 462–469.Google Scholar
2. Douglas, R. G., Banach algebra techniques in operator theory, Academic Press, New York, 1972.Google Scholar
3. Dugundji, J., Topology, Allyn and Bacon, Boston, 1966.Google Scholar
4. Engelking, R., General topology, Heldermann, Berlin, 1989.Google Scholar
5. Gleason, A. M., A characterization of maximal ideals, J. Anal. Math. 19(1967), 171–172.Google Scholar
6. Jacobson, N. and Rickart, C. E., Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69(1950), 479–502.Google Scholar
7. Kadison, R. V., Isometries of operator algebras, Ann. of Math. 54(1951), 325–338.Google Scholar
8. Kahane, J. P. and Zelazko, W., A characterization of maximal ideals in commutative Banach algebras, Studia Math. 29(1968), 339–343.Google Scholar
9. Kaplansky, I., Semi-automorphisms of rings, Duke Math. J. 14(1947), 521–525.Google Scholar
10. Paulsen, V. I., Completely bounded maps and dilations, Longman Sci. Tech., Essex, 1986.Google Scholar
11. Russo, B., Linear mappings of operator algebras, Proc. Amer. Math. Soc. 17(1966), 1019–1022.Google Scholar
12. Russo, B. and Dye, H. A., A note on unitary operators in C*-algebras, Duke Math. J. 33( 1966), 413–416.Google Scholar
13. Stormer, E., On the Jordan structure of C*-algebras, Trans. Amer. Math. Soc. 120(1965), 438–447.Google Scholar