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Study of the Order Structure on the Set of Ring Norms

  • G. R. Belitskii
  • Yurii I. Lyubich
Chapter
  • 160 Downloads
Part of the Operator Theory: Advances and Applications book series (OT, volume 36)

Abstract

We remind the reader that a chain in an ordered set is, by definition, a totally ordered subset, i.e., one in which any two elements are comparable. In its turn, the set of all chains is ordered by inclusion and satisfies the conditions of Zorn’s Lemma, which therefore guarantees the existence of maximal chains.

Keywords

Order Structure Linear Span Opposite Inequality Maximal Chain Invertible Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag Basel 1988

Authors and Affiliations

  • G. R. Belitskii
    • 1
  • Yurii I. Lyubich
    • 2
  1. 1.Institute of Low TemperaturesKharkov, UkraineUSSR
  2. 2.University of KharkovKharkov, UkraineUSSR

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