We show that if T is a narrow operator (for the definition see below) 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.
Positivity – Springer Journals
Published: Jan 18, 2003
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