Narrow operators and the Daugavet property for ultraproducts

Dmitriy Bilik, Vladimir Kadets, Roman Shvidkoy, Dirk Werner

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We show that if T is a narrow operator (for the definition see below) on X = X11 X2 or X = X1 ⊕∞ X2 then the restrictions to X 1 and X 2 are narrow and conversely. We also characterise by a version of the Daugavet property for positive operators on Banach lattices which unconditional sums of Banach spaces inherit the Daugavet property and we study the Daugavet property for ultraproducts.

Original languageEnglish (US)
Pages (from-to)45-62
Number of pages18
Issue number1
StatePublished - Mar 2005
Externally publishedYes

Bibliographical note

Funding Information:
The work of V.K. was supported by a grant from the Alexander-von-Humboldt Stiftung.


  • Daugavet property
  • Narrow operator
  • Strong Daugavet operator
  • Ultraproducts of Banach spaces


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