Let X and Y be Banach spaces. An operator G: X → Y is a Daugavet center if ‖G +T‖ = ‖G‖+‖T‖ for every rank-1 operator T. For every Daugavet center G we consider a certain set of operators acting from X, so-called G-narrow operators. We prove that if J is the natural embedding of Y into a Banach space E, then E can be equivalently renormed so that an operator T is (J ○ G)-narrow if and only if T is G-narrow. We study G-rich subspaces of X: Z ⊂ X is called G-rich if the quotient map q: X → X/Z is G-narrow.
@article{bwmeta1.element.doi-10_2478_s11533-013-0266-0,
author = {Tetiana Ivashyna},
title = {G-narrow operators and G-rich subspaces},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {1677-1688},
zbl = {1304.46011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0266-0}
}
Tetiana Ivashyna. G-narrow operators and G-rich subspaces. Open Mathematics, Tome 11 (2013) pp. 1677-1688. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0266-0/
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