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Octahedrality in Lipschitz free Banach spaces

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arxiv 1512.03558 v2 pith:RDSJHJKI submitted 2015-12-11 math.FA

Octahedrality in Lipschitz free Banach spaces

classification math.FA
keywords spacebanachmetrichypotheseslipschitzoctahedralityspacestopological
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The aim of this note is to study octahedrality in vector valued Lipschitz-free Banach spaces on a metric space under topological hypotheses on it. As a consequence, we get that the space of Lipschitz functions on a metric space valued in a dual Banach space satisfies the weak-star strong diameter two property, under natural topological hipothesess on the metric space. Also, we show an example proving that these hypotheses are optimal.

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