On the quasi-weak drop property

J. H. Qiu. "On the quasi-weak drop property." Studia Mathematica 151.2 (2002): 187-194. <http://eudml.org/doc/284652>.

@article{J2002,
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.},
author = {J. H. Qiu},
journal = {Studia Mathematica},
keywords = {Fréchet space; reflexive space; quasi-weak drop property; weakly compact set},
language = {eng},
number = {2},
pages = {187-194},
title = {On the quasi-weak drop property},
url = {http://eudml.org/doc/284652},
volume = {151},
year = {2002},
}

TY - JOUR
AU - J. H. Qiu
TI - On the quasi-weak drop property
JO - Studia Mathematica
PY - 2002
VL - 151
IS - 2
SP - 187
EP - 194
AB - 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.
LA - eng
KW - Fréchet space; reflexive space; quasi-weak drop property; weakly compact set
UR - http://eudml.org/doc/284652
ER -