Francisco Javier García‐Pacheco
Abstract
In this short note we prove that every real Banach space with separable dual can be equivalently renormed so that the set of non-norm-attaining functionals on it is nowhere dense. This solves a question proposed by Enflo.
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In this short note we prove that every real Banach space with separable dual can be equivalently renormed so that the set of non-norm-attaining functionals on it is nowhere dense. This solves a question proposed by Enflo.
Key concepts: Separable space, Banach space, Norm (philosophy), Mathematics, Nowhere dense set, Dual norm, Pure mathematics, Set (abstract data type)