The generalized Day norm. Part II. Applications
Journal Title: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica - Year 2017, Vol 71, Issue 2
Abstract
In this paper we prove that for each 1<p,p~<∞, the Banach space (lp~,∥⋅∥p~) can be equivalently renormed in such a way that the Banach space (lp~,∥⋅∥L,α,β,p,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 l2 with the Day norm. We also show that the Banach space (lp~,∥⋅∥L,α,β,p,p~) has the weak fixed point property for nonexpansive mappings.
Authors and Affiliations
Monika Budzyńska, Aleksandra Grzesik, Mariola Kot
Keywords
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- EP ID EP305645
- DOI 10.17951/a.2017.71.2.51
- Views 111
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