Fragmentability of the Dual of a Banach Space with Smooth Bump

Kortezov, I.. "Fragmentability of the Dual of a Banach Space with Smooth Bump." Serdica Mathematical Journal 24.2 (1998): 187-198. <http://eudml.org/doc/11589>.

@article{Kortezov1998,
abstract = {We prove that if a Banach space X admits a Lipschitz β-smooth bump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating a topology, which is stronger than the τβ -topology. We also use this to prove that if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X is sigma-fragmentable.},
author = {Kortezov, I.},
journal = {Serdica Mathematical Journal},
keywords = {Smooth Bump; Fragmentability; Sigma-Fragmentability; smooth bump; fragmentability; sigma-fragmentability; generic differentiability; dual; predual; bornology; weak Asplund; equivalent Gâteaux smooth norm; Gâteaux bornology},
language = {eng},
number = {2},
pages = {187-198},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Fragmentability of the Dual of a Banach Space with Smooth Bump},
url = {http://eudml.org/doc/11589},
volume = {24},
year = {1998},
}

TY - JOUR
AU - Kortezov, I.
TI - Fragmentability of the Dual of a Banach Space with Smooth Bump
JO - Serdica Mathematical Journal
PY - 1998
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 24
IS - 2
SP - 187
EP - 198
AB - We prove that if a Banach space X admits a Lipschitz β-smooth bump function, then (X ∗ , weak ∗ ) is fragmented by a metric, generating a topology, which is stronger than the τβ -topology. We also use this to prove that if X ∗ admits a Lipschitz Gateaux-smooth bump function, then X is sigma-fragmentable.
LA - eng
KW - Smooth Bump; Fragmentability; Sigma-Fragmentability; smooth bump; fragmentability; sigma-fragmentability; generic differentiability; dual; predual; bornology; weak Asplund; equivalent Gâteaux smooth norm; Gâteaux bornology
UR - http://eudml.org/doc/11589
ER -