On the local moduli of squareness
Tom 184 / 2008
Studia Mathematica 184 (2008), 175-189 MSC: Primary 46B10, 46B20; Secondary 46B03. DOI: 10.4064/sm184-2-6
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. Przes/lawski 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.