Journal of Soviet Mathematics

, Volume 36, Issue 3, pp 414–416 | Cite as

Duality in spectral optimization and numerical ranges of a family of self-adjoint operators

  • Yu. Sh. Abramov


One gives results which complement the author's investigation, published in Dokl. Akad. Nauk SSSR,255, No. 4, 777–780 (1980). One establishes the relationship of the fundamental condition ensuring the duality relation between the direct and the dual problems in spectral optimization problems with the geometry of the numerical ranges of certain families of self-adjoint operators.


Nauk SSSR Dual Problem Duality Relation Numerical Range Fundamental Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    Yu. Sh. Abramov, “Duality in extremal problems generated by spectral problems for operator pencils,” Dokl. Akad. Nauk SSSR,255, No. 4, 777–780 (1980).Google Scholar
  2. 2.
    Yu. Sh. Abramov, “Variational principles for nonlinear eigenvalue problems,” Funkts. Anal. Prilozhen.,7, No. 4, 76–77 (1973).Google Scholar
  3. 3.
    Yu. Sh. Abramov, “On the theory of nonlinear eigenvalue problems,” Dokl. Akad. Nauk SSSR,212, No. 1, 11–14 (1973).Google Scholar
  4. 4.
    Yu. Sh. Abramov, “Variational properties of the eigenvalues of certain problems that are nonlinear with respect to the parameter,” Izv. Akad. Nauk ArmSSR,11, No. 1, 23–39 (1974).Google Scholar
  5. 5.
    E. H. Rogers, “A minimax theory for overdamped systems,” Arch. Rational. Mech. Anal.,16, 89–96 (1964).Google Scholar
  6. 6.
    Yu. Sh. Abramov, “Numerical ranges, zones, and spectra of families of self-adjoint operators,” Dokl. Akad. Nauk SSSR,257, No. 5, 1033–1037 (1981).Google Scholar

Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • Yu. Sh. Abramov

There are no affiliations available

Personalised recommendations