We give an example of a Banach lattice with a non-convex modulus of monotonicity, which disproves a claim made in the literature. Results on preservation of the non-strict Opial property and Opial property under passing to general direct sums of Banach spaces are established.
@article{bwmeta1.element.ojs-doi-10_17951_a_2017_71_2_69,
author = {Joanna Markowicz and Stanis\l aw Prus},
title = {Properties of modulus of monotonicity and Opial property in direct sums},
journal = {Annales Universitatis Mariae Curie-Sk\l odowska, sectio A -- Mathematica},
volume = {71},
year = {2017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2017_71_2_69}
}
Joanna Markowicz; Stanisław Prus. Properties of modulus of monotonicity and Opial property in direct sums. Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 71 (2017) . http://gdmltest.u-ga.fr/item/bwmeta1.element.ojs-doi-10_17951_a_2017_71_2_69/
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