Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Vicente Montesinos

Instituto de Matemática Pura y Aplicada, Universitat Politècnica, Camino de Vera, 46022 Valencia, Spain

vmontesinos@mat.upv.es

Keywords

  • Property alpha
  • drop property
  • weak compactness
  • index of non-compactness

Mathematics Subject Classification

46B20; 46B50

References

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Suggested citation

I. Monterde, V. Montesinos. “Property (α) on Locally Convex Spaces.” Journal of Convex Analysis 25 (2018), No. 3, 1013–1017. https://doi.org/10.68381/jca25064

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press.