Narrow operators and the Daugavet property for ultraproducts

Narrow operators and the Daugavet property for ultraproducts 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

Narrow operators and the Daugavet property for ultraproducts

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Kluwer Academic Publishers
Copyright © 2005 by Springer
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
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