The generalized Day norm. Part II. Applications

Monika Budzyńska; Aleksandra Grzesik; Mariola Kot

Monika Budzyńska ; Aleksandra Grzesik ; Mariola Kot

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica, Tome 71 (2017), / Harvested from The Polish Digital Mathematics Library

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Résumé

In this paper we prove that for each $1 < p, \tilde{p} < \infty$ , the Banach space $(l^{\tilde{p}}, {∥\cdot∥}_{\tilde{p}})$ can be equivalently renormed in such a way that the Banach space $(l^{\tilde{p}}, {∥\cdot∥}_{L, α, β, p, \tilde{p}})$ is LUR and has a diametrically complete set with empty interior. This result extends the Maluta theorem about existence of such a set in $l^{2}$ with the Day norm. We also show that the Banach space $(l^{\tilde{p}}, {∥\cdot∥}_{L, α, β, p, \tilde{p}})$ has the weak fixed point property for nonexpansive mappings.

Publié le : 2017-01-01
EUDML-ID : urn:eudml:doc:289770

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     year = {2017},
     language = {en},
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Monika Budzyńska; Aleksandra Grzesik; Mariola Kot. The generalized Day norm. Part II. Applications. 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_51/

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