On the local moduli of squareness

Volume 184 / 2008

Antonio J. Guirao 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.


  • Antonio J. GuiraoDepartamento de Matemáticas
    Universidad de Murcia
    30100 Espinardo (Murcia), Spain

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