A Note on Universal Operators

Research output: Chapter in Book/Report/Conference proceedingConference contribution


An operator T is called universal for the complement of the ideal A if T does not belong to A, and factors through every element of the complement of A. We show that the complements of many ideals (such as the ideal of strictly (co)singular operators, or any maximal normed ideal) have no universal operators. On the other hand, the complement of the ideal of finitely strictly singular operators has a universal operator. Moreover, we show that, for many ideals A, any positive operator which factors positively through any positive member of the complement of A must be compact.
Original languageEnglish (US)
Title of host publicationOrdered Structures and Applications
Subtitle of host publicationPositivity VII (Zaanen Centennial Conference), 22-26 July 2013, Leiden, the Netherlands
EditorsMarcel de Jeu, Ben de Pagter, Onno van Gaans, Mark Veraar
ISBN (Electronic)9783319278421
ISBN (Print)9783319278407, 9783319802282
StatePublished - 2016

Publication series

NameTrends in Math
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X


  • Operator ideal
  • positive operator
  • universal operator


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