Geodesic
The generalized Day norm. Part II. Applications
Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 2.

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In this paper we prove that for each 1 lt; p, p̃ lt; ∞, the Banach space (l^p̃, ·_p̃) can be equivalently renormed in such a way that  the Banach space (l^p̃,·_L,α,β,p,p̃) 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^p̃,·_L,α,β,p,p̃) has the weak fixed point property for nonexpansive mappings.
Mots-clés : Diametrically complete set, Day norm, fixed point, Kadec-Klee property, LUR space, nonexpansive mapping, non-strict Opial property, 1-unconditional Schauder bases 
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Budzyńska, Monika; Grzesik, Aleksandra; Kot, Mariola. The generalized Day norm. Part II. Applications. Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 71 (2017) no. 2. https://geodesic-test.mathdoc.fr/item/AUM_2017_71_2_a7/

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