Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-22T18:13:58.029Z Has data issue: false hasContentIssue false
  • English
  • Français

Normal-Preserving Linear Mappings

Published online by Cambridge University Press:  20 November 2018

Matej Brešar  and
Peter Šemrl
Matej Brešar
Affiliation:
Department of Mathematics, University of Maribor PF, Koroška 160 62000 Maribor Slovenia
Peter Šemrl
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19, 61000 Ljubljana, Slovenia
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.

Let H be a Hilbert space, dim H ≥ 3, and B(H) the algebra of all bounded linear operators on H. We characterize bijective linear mappings on B(H) that preserve normal operators.

Keywords

47B1547D30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 3 , 01 September 1994 , pp. 306 - 309
Copyright
Copyright © Canadian Mathematical Society 1994

References

1. Bresar, M., Commuting traces of biadditive mappings, commutativity-preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335(1993), 525–546.Google Scholar
2. Chernoff, P. R., Representations, automorphisms and derivations of some operator algebras, J. Funct. Anal. 12(1973), 275–289.Google Scholar
3. Choi, M. D., Jafarian, A. A. and Radjavi, H., Linear Maps Preserving Commutativity, Linear Algebra Appl. 87(1987),227–241.Google Scholar
4. Jacobson, N., VI-Algebras, Lecture Notes in Math. 441, Springer-Verlag, Berlin, 1975.Google Scholar
5. Kunicki, C. M. and Hill, R. D., Normal-preserving Linear Transformations, Linear Algebra Appl. 170(1992), 107–115.Google Scholar
6. Li, C. K. and Tsing, N. K., Linear preserver problems: A brief introduction and some special techniques, Linear Algebra Appl. 162-164(1992), 217–235.Google Scholar
7. Mathieu, M., Rings of quotients of ultraprime Banach algebras with applications to elementary operators, Proc. Centre Math. Anal. Austral. Nat. Univ. 21(1989), 297–317.Google Scholar
8. Radjavi, H. and Rosenthal, P., Invariant Subspaces, Ergeb. Math. Grenzeb. 77, Springer Verlag, New York, 1973.Google Scholar