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Matematicheskie Zametki, 2007, Volume 82, Issue 3, Pages 459–468
DOI: https://doi.org/10.4213/mzm3993
(Mi mzm3993)
 

This article is cited in 6 scientific papers (total in 6 papers)

An Eigenvector Existence Theorem in Idempotent Analysis

G. B. Shpiz

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University
Full-text PDF (406 kB) Citations (6)
References:
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.
Received: 22.11.2006
Revised: 09.02.2007
English version:
Mathematical Notes, 2007, Volume 82, Issue 3, Pages 410–417
DOI: https://doi.org/10.1134/S0001434607090131
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: G. B. Shpiz, “An Eigenvector Existence Theorem in Idempotent Analysis”, Mat. Zametki, 82:3 (2007), 459–468; Math. Notes, 82:3 (2007), 410–417
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm3993
  • https://www.mathnet.ru/eng/mzm/v82/i3/p459
  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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