Browsing by Subject "Renorming"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Publication
    Open Access
    Kadec norms and Borel sets in a Banach space
    (Institute of Mathematics. Polish Academie of Sciences, 1999) Raja Baño, Matías; Matemáticas
    We introduce a property for a couple of topologies that allows us to give simple proofs of some classic results about Borel sets in Banach spaces by Edgar, Schachermayer and Talagrand as well as some new results. We characterize the existence of Kadec type renormings in the spirit of the new results for LUR spaces by Moltó, Orihuela and Troyanski.
  • Thumbnail Image
    Publication
    Embargo
    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.
  • Thumbnail Image
    Publication
    Embargo
    Uniformly convex renormings and generalized cotypes
    (Elsevier, 2021) Raja Baño, Matías; García-Lirola, Luis Carlos; Matemáticas
    We are concerned about improvements of the modulus of convexity by renormings of a super-reflexive Banach space. Typically optimal results are beyond Pisier’s power functions bounds tp, with p ≥2, and they are related to the notion of generalized cotype. We obtain an explicit upper bound for all the moduli of convexity of equivalent renormings and we show that if this bound is equivalent to t2, the best possible, then the space admits a renorming with modulus of power type 2. We show that a UMD space admits a renormings with modulus of convexity bigger, up to a multiplicative constant, than its cotype. We also prove the super-multiplicativity of the supremum of the set of cotypes.