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Properties of modulus of monotonicity and Opial property in direct sums

Joanna Markowicz; Stanisław Prus — 2017

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

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.

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