Preprint No. A-01-15

Dmitriy Bilik, Vladimir Kadets, Roman Shvidkoy, Dirk Werner

Narrow operators and the Daugavet property for ultraproducts

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.

Keywords: Daugavet property, narrow operator, strong Daugavet operator, ultraproducts of Banach spaces

Mathematics Subject Classification (MSC2000): 46B04; 46B08, 46B20, 46M07

Language: ENG

Available: Pr-A-01-15.ps

Contact: Dirk Werner, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (werner@math.fu-berlin.de)

[Home Page] - [Up] - [Search] - [Help] - Created: 20010628 -