It is known that there is a continuous linear functional on L ∞ which is not narrow. On the other hand, every order-to-norm continuous AM-compact operator from L ∞(μ) to a Banach space is narrow. We study order-to-norm continuous operators acting from L ∞(μ) with a finite atomless measure μ to a Banach space. One of our main results asserts that every order-to-norm continuous operator from L ∞(μ) to c 0(Γ) is narrow while not every such an operator is AM-compact.
@article{bwmeta1.element.doi-10_2478_s11533-009-0047-y,
author = {Irina Krasikova and Miguel Mart\'\i n and Javier Mer\'\i\ and Vladimir Mykhaylyuk and Mikhail Popov},
title = {On order structure and operators in L $\infty$($\mu$)},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {683-693},
zbl = {1198.47051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0047-y}
}
Irina Krasikova; Miguel Martín; Javier Merí; Vladimir Mykhaylyuk; Mikhail Popov. On order structure and operators in L ∞(μ). Open Mathematics, Tome 7 (2009) pp. 683-693. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0047-y/
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