# Fragmentability of the Dual of a Banach Space with Smooth Bump

Serdica Mathematical Journal (1998)

- Volume: 24, Issue: 2, page 187-198
- ISSN: 1310-6600

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topKortezov, 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 -

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