Journal of Convex Analysis 25 (2018), No. 3, 1013--1017
Copyright Heldermann Verlag 2018
Property (α) on Locally Convex Spaces
Ignacio Monterde
Universitat Politécnica, Camino de Vera, 46022 Valencia, Spain
nachomonterde@gmail.com
Vicente Montesinos
Instituto de Matemática Pura y Aplicada, Universitat Politécnica, Camino de Vera, 46022 Valencia, Spain
vmontesinos@mat.upv.es
We study property (α) for closed convex subsets of locally convex spaces and we prove that the quasi drop property implies property (α). Moreover, if the locally convex space is complete, property (α) implies weak compactness. Thus, if every closed, convex and bounded subset of a complete locally convex spaces E has property (α), then E is semi-reflexive.
Keywords: Property alpha, drop property, weak compactness, index of non-compactness.
MSC: 46B20; 46B50
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