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2017 | 71 | 2 |
Tytuł artykułu

The generalized Day norm. Part II. Applications

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EN
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EN
In this paper we prove that for each \(1< p, \tilde{p} < \infty\), the Banach space \((l^{\tilde{p}}, \left\|\cdot\right\|_{\tilde{p}})\) can be equivalently renormed in such a way that  the Banach space \((l^{\tilde{p}},\left\|\cdot\right\|_{L,\alpha,\beta,p,\tilde{p}})\) 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 \((l^{\tilde{p}},\left\|\cdot\right\|_{L,\alpha,\beta,p,\tilde{p}})\) has the weak fixed point property for nonexpansive mappings.
Rocznik
Tom
71
Numer
2
Opis fizyczny
Daty
wydano
2017
online
2017-12-18
Bibliografia
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.ojs-doi-10_17951_a_2017_71_2_51
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