Abstract. We prove that a suitable renorming of l_2, known to be LUR and to lack normal structure, contains diametrically complete sets whose interior is empty. As a consequence, we answer in the negative the question, opened by Moreno, Papini and Phelps in 2006, whether diametrically complete sets in LUR spaces must be, in some sense, locally uniformly rotund.
A diametrically complete set with empty interior in a reflexive LUR space
MALUTA, ELISABETTA
2017-01-01
Abstract
Abstract. We prove that a suitable renorming of l_2, known to be LUR and to lack normal structure, contains diametrically complete sets whose interior is empty. As a consequence, we answer in the negative the question, opened by Moreno, Papini and Phelps in 2006, whether diametrically complete sets in LUR spaces must be, in some sense, locally uniformly rotund.File in questo prodotto:
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