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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-2-6,
author = {J. H. Qiu},
title = {On the quasi-weak drop property},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {187-194},
zbl = {1012.46006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-2-6}
}
J. H. Qiu. On the quasi-weak drop property. Studia Mathematica, Tome 151 (2002) pp. 187-194. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm151-2-6/