%0 Journal Article
%T Narrow operators and the Daugavet property for ultraproducts
%A Dmitriy Bilik
%A Vladimir Kadets
%A Roman Shvidkoy
%A Dirk Werner
%J Mathematics
%D 2001
%I arXiv
%X We show that if $T$ is a narrow operator on $X=X_{1}\oplus_{1} X_{2}$ or $X=X_{1}\oplus_{\infty} X_{2}$, 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.
%U http://arxiv.org/abs/math/0107132v1