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Narrow operators and the Daugavet property for ultraproducts

Dmitriy Bilik·Vladimir Kadets·Roman Shvidkoy·Dirk Werner
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Abstract

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.

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Dmitriy Bilik, Vladimir Kadets, Roman Shvidkoy, Dirk Werner. 2001-07-19. Narrow operators and the Daugavet property for ultraproducts. https://doi.org/10.1007/s11117-003-9339-9

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