理想空间中2-完全非负算子的K-Krein定理
Gantmakher-Krein theorem for 2-totally nonnegative operators in ideal spaces
摘要：
研究了作用在理想空间$X(Ω)$中的完全连续非负线性算子$A$的张量和外平方。证明了张量平方$A \otimes A$的点谱（可能零除外）用初始算子$A$的谱表示的定理.在外平方$A\wedge A$也非负的附加条件下，证明了全连续非负算子$A$的第二个（按模）正本征值$λ_2$或一对复伴随本征值的存在性.
英文摘要：
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.
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