We introduce the notions of pointwise modulus of squareness and local modulus of squareness of a normed space X. This answers a question of C. Benítez, K. Przesławski and D. Yost about the definition of a sensible localization of the modulus of squareness. Geometrical properties of the norm of X (Fréchet smoothness, Gâteaux smoothness, local uniform convexity or strict convexity) are characterized in terms of the behaviour of these moduli.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-2-6,
author = {Antonio J. Guirao},
title = {On the local moduli of squareness},
journal = {Studia Mathematica},
volume = {187},
year = {2008},
pages = {175-189},
zbl = {1139.46010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-2-6}
}
Antonio J. Guirao. On the local moduli of squareness. Studia Mathematica, Tome 187 (2008) pp. 175-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm184-2-6/