It is an open question when the direct sum of normed spaces inherits uniform rotundity in every direction from the factor spaces. M. Smith [4] showed that, in general, the answer is negative. The purpose of this paper is to carry out a complete study of Smith's counterexample.
@article{urn:eudml:doc:38630,
title = {Smith's counterexample about uniform rotundity in every direction.},
journal = {Extracta Mathematicae},
volume = {15},
year = {2000},
pages = {257-263},
zbl = {0987.46013},
mrnumber = {MR1823651},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38630}
}
Fernández, Manuel; Palacios, Isidro. Smith's counterexample about uniform rotundity in every direction.. Extracta Mathematicae, Tome 15 (2000) pp. 257-263. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38630/