Narrow operators and the Daugavet property for ultraproducts
Dmitriy Bilik, Vladimir Kadets, Roman Shvidkoy, Dirk Werner
Abstract
We show that if T is a narrow operator on X=X11 X2 or X=X1∞ X2, then the restrictions to X1 and X2 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.
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