On the local moduli of squareness

Antonio J. Guirao. "On the local moduli of squareness." Studia Mathematica 184.2 (2008): 175-189. <http://eudml.org/doc/285367>.

@article{AntonioJ2008,
abstract = {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.},
author = {Antonio J. Guirao},
journal = {Studia Mathematica},
keywords = {Banach spaces; locally uniformly rotund norms; Fréchet smooth norms; strictly convex norms; Gâteaux smooth norms; modulus of squareness},
language = {eng},
number = {2},
pages = {175-189},
title = {On the local moduli of squareness},
url = {http://eudml.org/doc/285367},
volume = {184},
year = {2008},
}

TY - JOUR
AU - Antonio J. Guirao
TI - On the local moduli of squareness
JO - Studia Mathematica
PY - 2008
VL - 184
IS - 2
SP - 175
EP - 189
AB - 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.
LA - eng
KW - Banach spaces; locally uniformly rotund norms; Fréchet smooth norms; strictly convex norms; Gâteaux smooth norms; modulus of squareness
UR - http://eudml.org/doc/285367
ER -