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)
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