Journal of Convex Analysis 22 (2015), No. 3, 871--888
Copyright Heldermann Verlag 2015
The Degree of Convex Nondensifiability in Banach Spaces
Gonzalo Garcia Macias
Dpto. Analisis Matematico, Universidad de Alicante, Ap. de Correos 99, 03080 Alicante, Spain
gonzalogarciamacias@gmail.com
Gaspar Mora Martinez
Dpto. Analisis Matematico, Universidad de Alicante, Ap. de Correos 99, 03080 Alicante, Spain
gaspar.mora@ua.es
It is shown in this paper that the notion of α-dense curve in a bounded set of a metric space produces a degree of nondensifiability φd which extended to convex hulls of bounded sets in a Banach space generates a measure of noncompactness (briefly MNC) Φ that we will call degree of convex nondensifiability. We also prove that Φ dominates any other MNC and, in particular, dominates the MNC of Hausdorff of the best possible form in infinite dimensional Banach spaces.
Keywords: alpha-dense curves, degree of nondensifiability, degree of convex nondensifiability, measures of noncompactness.
MSC: 47H08, 46B20
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