Uniformly convex renormings and generalized cotypes

García-Lirola, L.C. (Universidad de Zaragoza) ; Raja, M.

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.aim.2021.107679

Año: 2021

Publicado en: Advances in Mathematics 383 (2021), 107679 [23 pp.]
ISSN: 0001-8708

Factor impacto JCR: 1.675 (2021)

Categ. JCR: MATHEMATICS rank: 59 / 333 = 0.177 (2021) - Q1 - T1

Factor impacto CITESCORE: 2.6 - Mathematics (Q2)

Factor impacto SCIMAGO: 1.935 - Mathematics (miscellaneous) (Q1)

Financiación: info:eu-repo/grantAgreement/ES/MINECO/ MTM2017-83262-C2-2-P

Tipo y forma: Article (Published version)

Área (Departamento): Área Análisis Matemático (Dpto. Matemáticas)