Smooth renormings of the Lebesgue-Bochner function space L¹(μ,X)

Marián Fabian, and Sebastián Lajara. "Smooth renormings of the Lebesgue-Bochner function space L¹(μ,X)." Studia Mathematica 209.3 (2012): 247-265. <http://eudml.org/doc/285720>.

@article{MariánFabian2012,
abstract = {We show that, if μ is a probability measure and X is a Banach space, then the space L¹(μ,X) of Bochner integrable functions admits an equivalent Gâteaux (or uniformly Gâteaux) smooth norm provided that X has such a norm, and that if X admits an equivalent Fréchet (resp. uniformly Fréchet) smooth norm, then L¹(μ,X) has an equivalent renorming whose restriction to every reflexive subspace is Fréchet (resp. uniformly Fréchet) smooth.},
author = {Marián Fabian, Sebastián Lajara},
journal = {Studia Mathematica},
keywords = {Lebesgue-Bochner space ; smooth norm; Orlicz-Bochner norm; reflexive subspaces of ; Fréchet smooth norm; uniformly smooth norm; uniformly Fréchet smooth norm},
language = {eng},
number = {3},
pages = {247-265},
title = {Smooth renormings of the Lebesgue-Bochner function space L¹(μ,X)},
url = {http://eudml.org/doc/285720},
volume = {209},
year = {2012},
}

TY - JOUR
AU - Marián Fabian
AU - Sebastián Lajara
TI - Smooth renormings of the Lebesgue-Bochner function space L¹(μ,X)
JO - Studia Mathematica
PY - 2012
VL - 209
IS - 3
SP - 247
EP - 265
AB - We show that, if μ is a probability measure and X is a Banach space, then the space L¹(μ,X) of Bochner integrable functions admits an equivalent Gâteaux (or uniformly Gâteaux) smooth norm provided that X has such a norm, and that if X admits an equivalent Fréchet (resp. uniformly Fréchet) smooth norm, then L¹(μ,X) has an equivalent renorming whose restriction to every reflexive subspace is Fréchet (resp. uniformly Fréchet) smooth.
LA - eng
KW - Lebesgue-Bochner space ; smooth norm; Orlicz-Bochner norm; reflexive subspaces of ; Fréchet smooth norm; uniformly smooth norm; uniformly Fréchet smooth norm
UR - http://eudml.org/doc/285720
ER -