Gantmakher-Krein theorem for 2-totally nonnegative operators in ideal spaces
Loading...
Date
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
The tensor and exterior squares of a completely continuous non-negative linear operator $A$ acting in the ideal space $X(Ω)$ are studied. The theorem representing the point spectrum (except, probably, zero) of the tensor square $A \otimes A$ in the terms of the spectrum of the initial operator $A$ is proved. The existence of the second (according to the module) positive eigenvalue $λ_2$, or a pair of complex adjoint eigenvalues of a completely continuous non-negative operator $A$ is proved under the additional condition, that its exterior square $A\wedge A$ is also nonnegative.
13 pages
13 pages