Skip to main content
SpringerLink
Log in

On complementary matrix algebras

  • Published:
Integral Equations and Operator Theory Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. Gohberg, P. Lancaster, and L. Rodman, Invariant Subspaces of Matrices with Applications, John Wiley & Sons, New York, 1986.

    Google Scholar 

  2. N. Jacobson, Lectures in Abstract Algebra II: Linear Algebra, D. Van Nostrand, Princeton, 1953.

    Google Scholar 

  3. J.F. Watters, Block Triangularization of algebras of matrices, Linear Alg. & Appl. 32 (1980), 3–7.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Toronto, M5S 1A1, Toronto, Canada

    Man-Duen Choi & Peter Rosenthal

  2. Dept. of Math., Stats. & Comp. Sci., Dalhousie University, B3H 3J5, Halifax, Canada

    Heydar Radjavi

Authors
  1. Man-Duen Choi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heydar Radjavi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peter Rosenthal
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported by the Natural Sciences and Engineering Research Council of Canada.

Rights and permissions

Reprints 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

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01193754

Keywords

Search

Navigation