This article is cited in 6 papers

An Eigenvector Existence Theorem in Idempotent Analysis

G. B. Shpiz

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Abstract: 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, homomorphism, ideompotent semiring, linear functional.

UDC: 517.9

Received: 22.11.2006
Revised: 09.02.2007

DOI: 10.4213/mzm3993

 English version: Mathematical Notes, 2007, 82:3, 410–417

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