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Mathematical Notes

, Volume 69, Issue 5–6, pp 696–729 | Cite as

Idempotent Functional Analysis: An Algebraic Approach

  • G. L. Litvinov
  • V. P. Maslov
  • G. B. Shpiz
Article

Abstract

This paper is devoted to Idempotent Functional Analysis, which is an “abstract” version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a brief survey of the basic ideas of Idempotent Analysis. The correspondence between concepts and theorems of traditional Functional Analysis and its idempotent version is discussed in the spirit of N. Bohr's correspondence principle in quantum theory. We present an algebraic approach to Idempotent Functional Analysis. Basic notions and results are formulated in algebraic terms; the essential point is that the operation of idempotent addition can be defined for arbitrary infinite sets of summands. We study idempotent analogs of the basic principles of linear functional analysis and results on the general form of a linear functional and scalar products in idempotent spaces.

Idempotent Analysis Functional Analysis linear functional scalar product 

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • G. L. Litvinov
    • 1
  • V. P. Maslov
    • 2
  • G. B. Shpiz
    • 1
  1. 1.International Sophus Lie CenterRussia
  2. 2.M. V. Lomonosov Moscow State UniversityRussia

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