Let ℛ denote some kind of rotundity, e.g., the uniform rotundity. Let X admit an ℛ-norm and let Y be a reflexive subspace of X with some ℛ-norm ∥·∥. Then we are able to extend ∥·∥ from Y to an ℛ-norm on X.
@article{bwmeta1.element.bwnjournal-article-smv112i3p203bwm,
author = {M. Fabian},
title = {On an extension of norms from a subspace to the whole Banach space keeping their rotundity},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {203-211},
zbl = {0824.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv112i3p203bwm}
}
Fabian, M. On an extension of norms from a subspace to the whole Banach space keeping their rotundity. Studia Mathematica, Tome 113 (1995) pp. 203-211. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv112i3p203bwm/
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