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Metric characterization of first Baire class linear forms and octahedral norms

Gilles Godefroy
- 01 Jan 1989 - 
- Vol. 95, Iss: 1, pp 1-15
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This article is published in Studia Mathematica.The article was published on 1989-01-01 and is currently open access. It has received 85 citations till now. The article focuses on the topics: Baire measure & Baire space.

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On duality of diameter 2 properties

TL;DR: In this article, the stability properties of different types of octahedrality were studied, which, by duality, provide easier proofs of many known results on diameter 2 properties.
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Octahedral norms and convex combination of slices in Banach spaces

TL;DR: The relation between octahedral norms, Daugavet property and the size of convex combinations of slices in Banach spaces was studied in this article. But it was not shown that the norm of an arbitrary Banach space is octagonal unless, and only if, every convex combination of w ⁎ -slices in the dual unit ball has diameter 2.
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Chapter 18 – Renormings of Banach Spaces

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On strongly norm attaining Lipschitz maps

TL;DR: In this article, the authors study the set SNA (M, Y ) of Lipschitz maps from a complete pointed metric space M to a Banach space Y which attain their Lipschnitz norm (i.e. the supremum defining the Lipschenitz norm is a maximum).
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Octahedral norms in tensor products of Banach spaces

TL;DR: In this article, it was shown that in the presence of the metric approximation property octahedrality is preserved from a non-reflexive $L$-embedded Banach space taking projective tensor products.