Skip to main content
SpringerLink
Log in

Generalized inverses over Banach algebras

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

Abstract

LetA be a matrix over a complex commutative unital Banach algebra. We give necessary and sufficient conditions forA to have a generalized inverse. Moreover, if the Banach algebra has a symmetric involution, these are also necessary and sufficient conditions forA to admit the Moore-Penrose inverse.

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. Bapat, R.B., Rao, B.K.P.S. and Prasad, K.M.,Generalized Inverses Over Integral Domains, Linear Algebra Appl.140 (1990), 181–196.

    Google Scholar 

  2. Ben-Israel, A., Greville, T.N.E.,Generalized Inverses and Applications, Wiley, (1974).

  3. Rao, B.K.P.S.,On Generalized Inverses of Matrices over Integral Domains, Linear Algebra Appl.49 (1983), 179–189.

    Google Scholar 

  4. Bruening, J.T.,A New Formula for the Moore-Penrose Inverse, in Current Trends in Matrix Theory (F. Uhlig and R. Grone, Ed.), Elsevier Science, (1987).

  5. Carleson, L.,Interpolations by Bounded Analytic Functions and the Corona Problem, Annals of Math.76 (1962), 547–559.

    Google Scholar 

  6. Gelfand, I., Raikov, D. and Shilov, G.,Commutative Normed Rings, Chelsea (1964).

  7. Gohberg, I., Goldberg, S. and Kaashoek, M.A.,Classes of Linear Operators, Vol. 1, Operator Theory: Advances and Applications,49 (1990), Birkhauser Verlag, Basel.

    Google Scholar 

  8. Gohberg, I., Goldberg, S. and Kaashoek, M.A.,Classes of Linear Operators, Vol. 2, to appear.

  9. Gohberg, I., and Krupnik, N.Ya.,Einfuhrung in die Theorie der Eindimersionalen Singularen Integraloperatoren, Mathematische Reihe, Band 63, Birkhauser Verlag, Basel (1979).

    Google Scholar 

  10. Gohberg, I., Leiterer, J.,Factorization of operator Functions Relative to a Contour, II. Canonical factorization of operator functions closed to an identity, Math. Nachr.54 (1972), 41–74 (Russian).

    Google Scholar 

  11. Muir, T.,A Treatise on the Theory of Determinants, Dover (1960).

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742, College Park, MD, U.S.A.

    Danrun Huang

Authors
  1. Danrun Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Partially supported by NSF Grant DMS-8802593

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, D. Generalized inverses over Banach algebras. Integr equ oper theory 15, 454–469 (1992). https://doi.org/10.1007/BF01200329

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01200329

MSC 1991

Search

Navigation