TITLE

GANTMACHER-KREĬN THEOREM FOR 2 NONNEGATIVE OPERATORS IN SPACES OF FUNCTIONS

AUTHOR(S)
Kushel, O. Y.; Zabreiko, P. P.
PUB. DATE
January 2006
SOURCE
Abstract & Applied Analysis;2006, p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The existence of the second (according to the module) eigenvalue λ2 of a completely continuous nonnegative operator A is proved under the conditions that A acts in the space Lp(Ω) or C(Ω) and its exterior square A?A is also nonnegative. For the case when the operators A and A ∧ A are indecomposable, the simplicity of the first and second eigenvalues is proved, and the interrelation between the indices of imprimitivity of A and A ∧ A is examined. For the case when A and A ∧ A are primitive, the difference (according to the module) of λ1 and λ2 from each other and from other eigenvalues is proved.
ACCESSION #
24081216

 

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