Study of the Order Structure on the Set of Ring Norms

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


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.


Order Structure Linear Span Opposite Inequality Maximal Chain Invertible Operator 
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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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