Geodesic
An Eigenvector Existence Theorem in Idempotent Analysis
Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 459-468

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In this paper, we prove an eigenvector existence theorem for linear operators on abstract idempotent spaces in the framework of the algebraic approach. Earlier, an algebraic version of a similar statement was known only for operators in free finite-dimensional semimodules. The corresponding result for compact operators in semimodules of real continuous functions is known in the case of topological semimodules.
Keywords: abstract idempotent space, idempotent semimodule, idempotent semiring, idempotent semigroup, ordered set, ideompotent semiring, linear functional.
Mots-clés : homomorphism 
@article{MZM_2007_82_3_a12,
     author = {G. B. Shpiz},
     title = {An {Eigenvector} {Existence} {Theorem} in {Idempotent} {Analysis}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {459--468},
     publisher = {mathdoc},
     volume = {82},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a12/}
}
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G. B. Shpiz. An Eigenvector Existence Theorem in Idempotent Analysis. Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 459-468. http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a12/