A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies ||G + T|| = ||G|| + ||T||. We study the case when either X or Y is a sum X 1⊕F X 2 of two Banach spaces X 1 and X 2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X 1 and X 2 there exists a Daugavet center acting from X 1⊕F X 2, and the class of those F such that for some pair of spaces X 1 and X 2 there is a Daugavet center acting into X 1⊕F X 2. We also present several examples of such Daugavet centers.
@article{bwmeta1.element.doi-10_2478_s11533-010-0015-6,
author = {Tetiana Bosenko},
title = {Daugavet centers and direct sums of Banach spaces},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {346-356},
zbl = {1210.46009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0015-6}
}
Tetiana Bosenko. Daugavet centers and direct sums of Banach spaces. Open Mathematics, Tome 8 (2010) pp. 346-356. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0015-6/
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