Skip to main content
SpringerLink
Log in

Superconvexity of the spectral radius, and convexity of the spectral bound and the type

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

References

  1. Chernoff, P.R.: Product formulas, nonlinear semigroups, and addition of unbounded operators. Mem. Amer. Math. Soc.140 (1974)

  2. Cohen, J.E.: Convexity of the dominant eigenvalue of an essentially nonnegative matrix. Proc. Amer. Math. Soc.81, 657–658 (1981)

    Google Scholar 

  3. Donsker, M.D., Varadhan, S.R.S.: On a variational formula for the principal eigenvalue for operators with maximum principle. Proc. Nat. Acad. Sci. U.S.A.72, 780–783 (1975)

    Google Scholar 

  4. Donsker, M.D., Varadhan, S.R.S.: On the principal eigenvalue of second-order elliptic differential operators. Comm. Pure Appl. Math.29, 595–621 (1976)

    Google Scholar 

  5. Friedland, S.: Convex spectral functions. Linear and Multilinear Algebra9, 299–316 (1981)

    Google Scholar 

  6. Greiner, G., Voigt, J., Wolff, M.: On the spectral bound of the generator of semigroups of positive operators. Preprint 1981

  7. Hess, P., Kato, T.: On some linear and nonlinear eigenvalue problems with an indefinite weight function. Comm. Partial Differential Equations5, 999–1030 (1980)

    Google Scholar 

  8. Hille, E., Phillips, R.S.: Functional analysis and semi-groups. Amer. Math. Soc. Colloq. Publ. Vol. 31, Rev. Ed. Providence, Rhode Island: American Mathematical Society 1957

    Google Scholar 

  9. Holland, C.J.: A minimum principle for the principal eigenvalue for second-order linear elliptic equations with natural boundary conditions. Comm. Pure Appl. Math.31, 509–519 (1978)

    Google Scholar 

  10. Kato, T.: Perturbation theory for linear operators, 2nd Ed. Berlin-Heidelberg-New York: Springer 1980

    Google Scholar 

  11. Kato, T.: A spectral mapping theorem for the exponential function, and some counterexamples. Mathematical Research Center Technical Report #2316, Madison: University of Wisconsin 1982

    Google Scholar 

  12. Kingman, J.F.C.: A convexity property of positive matrices. Quart. J. Math. Oxford (2)12, 283–284 (1961)

    Google Scholar 

  13. Protter, M.H., Weinberger, H.F.: On the spectrum of general second order operators. Bull. Amer. Math. Soc.72, 251–255 (1966)

    Google Scholar 

  14. Schaefer, H.H.: Topological vecgor spaces. New York-Heidelberg-Berlin: Springer 1971

    Google Scholar 

  15. Walsh, B.: Positive approximation identities and lattice-ordered dual spaces. Manuscripta Math.14, 57–63 (1974)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 94720, Berkeley, California, U.S.A.

    Tosio Kato

Authors
  1. Tosio Kato
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kato, T. Superconvexity of the spectral radius, and convexity of the spectral bound and the type. Math Z 180, 265–273 (1982). https://doi.org/10.1007/BF01318910

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01318910

Keywords

Search

Navigation