Geodesic
The Gantmakher--Krein theorem for completely indecomposable operators in spaces of functions
Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 73-79

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For a completely continuous non-negative operator $A$ acting in the space $L_p(\Omega)$ or $C(\Omega)$ the existence of $k$ positive eigenvalues is proved under some additional conditions on its $j$-th $(1$ exterior power $\wedge^jA$. For the case where the operator $A$ is completely indecomposable, the simplicity of all non-zero eigenvalues is proved and the connection between the imprimitivity indices of $A$ and $\wedge^jA$ is examined. 
@article{TIMB_2006_14_2_a8,
     author = {O. Y. Kushel},
     title = {The {Gantmakher--Krein} theorem for completely indecomposable operators in spaces of functions},
     journal = {Trudy Instituta matematiki},
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     publisher = {mathdoc},
     volume = {14},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a8/}
}
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O. Y. Kushel. The Gantmakher--Krein theorem for completely indecomposable operators in spaces of functions. Trudy Instituta matematiki, Tome 14 (2006) no. 2, pp. 73-79. http://geodesic.mathdoc.fr/item/TIMB_2006_14_2_a8/