Gantmacher-Kreĭn theorem for 2 nonnegative operators in spaces of functions

O. Y. Kushel and P. P. Zabreiko

Abstract and Applied Analysis, 2006, vol. 2006, 1-15

Abstract:

The existence of the second (according to the module) eigenvalue λ 2 of a completely continuous nonnegative operator A is proved under the conditions that A acts in the space L p ( 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 λ 1 and λ 2 from each other and from other eigenvalues is proved.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:048132

DOI: 10.1155/AAA/2006/48132

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