Browsing by Subject "Banach spaces"

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    Locally uniformly rotund norms
    (Wiley, 1999) Raja Baño, Matías; Matemáticas
    Given a Banach space X and a norming subspace Z subset of X*, a geometrical method is introduced to characterize the existence of an equivalent sigma(X, Z)-lsc LUR norm on X. A new simple proof of the Theorem of Troyanski: every rotund space with a Kadec norm is LUR renormable, and a generalization of the Moltó, Orihuela and Troyanski characterization of the LUR renormability, are provided without probability arguments. Among other applications, it is shown that a dual Banach space with a w*-Kadec norm admits a dual LUR norm.