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On \({{\cal T}_{\!p}}\)-Locally Uniformly Rotund Norms

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Abstract

Linear topological characterizations of Banach spaces E ⊂ ℓ ∞ (Γ) which admit pointwise locally uniformly rotund norms are obtained. We introduce a new way to construct the norm with families of sliced sets. The topological properties described are related with the theory of generalized metric spaces, in particular with Moore spaces and σ-spaces. A non liner transfer is obtained, Question 6.16 in Moltó et al. (2009) is answered and some connections with Kenderov’s School of Optimization is presented in this paper.

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Authors and Affiliations

  1. Dpto. Matemáticas, Universidad de Murcia, 30.100 Espinardo, Murcia, Spain

    J. Orihuela

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  1. J. Orihuela
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Correspondence to J. Orihuela.

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Dedicated to Petar S. Kenderov on the occcasion of his 70th birthday.

This research was partially supported by MEC and FEDER project MTM2011-25377.

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Orihuela, J. On \({{\cal T}_{\!p}}\)-Locally Uniformly Rotund Norms. Set-Valued Var. Anal 21, 691–709 (2013). https://doi.org/10.1007/s11228-013-0254-3

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