Gantmacher-Krein Theorem for 2-totally Nonnegative Operators in Ideal Spaces
Olga Y. Kushel, П. П. Забрейко · Birkhäuser Basel eBooks · 2010
The tensor and exterior squares of a completely continuous nonnegative 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 ⊗ A) M in the terms of the spectrum of the initial operator A is proved. The existence of the second (according to the module) positive eigenvalue λ2, or a pair of complex conjugate eigenvalues of a completely continuous non-negative operator A is proved under the additional condition, that its exterior square (A ∧ A) M is also nonnegative.