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Dual spaces generated by the interior of the set of norm attaining functionals

Maria D. AcostaJulio Becerra GuerreroManuel Ruiz Galán — 2002

Studia Mathematica

We characterize some isomorphic properties of Banach spaces in terms of the set of norm attaining functionals. The main result states that a Banach space is reflexive as soon as it does not contain ℓ₁ and the dual unit ball is the w*-closure of the convex hull of elements contained in the "uniform" interior of the set of norm attaining functionals. By assuming a very weak isometric condition (lack of roughness) instead of not containing ℓ₁, we also obtain a similar result. As a consequence of the...

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