# 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Narrow operators and the Daugavet property for ultraproducts

, Volume 9 (1) – Jan 18, 2003
18 pages

/lp/springer_journal/narrow-operators-and-the-daugavet-property-for-ultraproducts-1U4LtZ0syY
Publisher
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-003-9339-9
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

PositivitySpringer Journals

Published: Jan 18, 2003

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