Abstract
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.
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Communicated by L. Rodman.
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Kushel, O.Y., Zabreiko, P.P. (2010). Gantmacher-Krein Theorem for 2-totally Nonnegative Operators in Ideal Spaces. In: Topics in Operator Theory. Operator Theory: Advances and Applications, vol 202. Birkhäuser Basel. https://doi.org/10.1007/978-3-0346-0158-0_22
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DOI: https://doi.org/10.1007/978-3-0346-0158-0_22
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