On the quasi-weak drop property
Volume 151 / 2002
Studia Mathematica 151 (2002), 187-194
MSC: 46A55, 46B20.
DOI: 10.4064/sm151-2-6
Abstract
A new drop property, the quasi-weak drop property, is introduced. Using streaming sequences introduced by Rolewicz, a characterisation of the quasi-weak drop property is given for closed bounded convex sets in a Fréchet space. From this, it is shown that the quasi-weak drop property is equivalent to weak compactness. Thus a Fréchet space is reflexive if and only if every closed bounded convex set in the space has the quasi-weak drop property.
