Abstract
It is proved that complementary algebras of linear operators on ℂn do not necessarily have nontrivial complementary invariant subspaces. This settles a conjecture of Gohberg, Lancaster, and Rodman in the negative. A positive result is also proved under certain additional hypotheses.
Similar content being viewed by others
References
I. Gohberg, P. Lancaster, and L. Rodman, Invariant Subspaces of Matrices with Applications, John Wiley & Sons, New York, 1986.
N. Jacobson, Lectures in Abstract Algebra II: Linear Algebra, D. Van Nostrand, Princeton, 1953.
J.F. Watters, Block Triangularization of algebras of matrices, Linear Alg. & Appl. 32 (1980), 3–7.
Author information
Authors and Affiliations
Additional information
This research was supported by the Natural Sciences and Engineering Research Council of Canada.
Rights and permissions
About this article
Cite this article
Choi, MD., Radjavi, H. & Rosenthal, P. On complementary matrix algebras. Integr equ oper theory 13, 165–174 (1990). https://doi.org/10.1007/BF01193754
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01193754