Narrow operators and the Daugavet property for ultraproducts

Details Narrow operators and the Daugavet property for ultraproducts Narrow operators and the Daugavet property for ultraproducts

2001-07-19

arxiv.org/abs/math/0107132v1

Positivity 9, no.1, 46-62 (2005)

Mathematics

Functional Analysis

15 pages

Scientific paper

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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