Mathematics and Statistics Vol. 3(1), pp. 1 - 6
DOI: 10.13189/ms.2015.030101
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Criteria for the Existence of Common Points of Spectra of Several Operator Pencils

R. M. Dzhabarzadeh ^*
Institute of Mathematics and Mechanics, National Academy of Science of Azerbaijan, Azerbaijan

ABSTRACT

In this paper we present two criteria for the existence of common eigen values of several operator pencils having discrete spectrum. One of the given criteria is proved by using analogs of resultant for several operator pencils; proof of the other criterion requires the use of the results of the multiparameter spectral theory. In both cases the number of operator pencils is finite, operator pencils act, generally speaking, in different Hilbert spaces.

KEYWORDS
Operator Pencils, Resultant of Two Operator Pencils, Hilbert Space, Common Eigenvalue, Kernel of Operator

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] R. M. Dzhabarzadeh , "Criteria for the Existence of Common Points of Spectra of Several Operator Pencils," Mathematics and Statistics, Vol. 3, No. 1, pp. 1 - 6, 2015. DOI: 10.13189/ms.2015.030101.

(b). APA Format:
R. M. Dzhabarzadeh (2015). Criteria for the Existence of Common Points of Spectra of Several Operator Pencils. Mathematics and Statistics, 3(1), 1 - 6. DOI: 10.13189/ms.2015.030101.