descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Mar 2005Embargo end date: 01 Jan 2001 English Publisher:Springer Science and Business Media LLCJournal:Positivity, volume 9, pages 45-62 (issn: 1385-1292, eissn: 1572-9281,

Authors: Dmitriy Bilik; Roman Shvidkoy; Vladimir Kadets; Dirk Werner;

doi: 10.1007/s11117-003-9339-9 , 10.48550/arxiv.math/0107132

arXiv: http://arxiv.org/abs/math/0107132

Narrow operators and the Daugavet property for ultraproducts

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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.

15 pages

Related Organizations

Freie Universität Berlin
Germany
V.N. Karazin Kharkiv National University
Ukraine
The University of Texas at Austin
United States
University of Missouri Health System
United States
University of Missouri
United States

Keywords

Mathematics - Functional Analysis, 46B04, 46B08, 46B20, 46M07, FOS: Mathematics, Functional Analysis (math.FA)

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