000150974 001__ 150974 000150974 005__ 20250221105702.0 000150974 0247_ $$2doi$$a10.1016/j.aim.2021.107679 000150974 0248_ $$2sideral$$a123956 000150974 037__ $$aART-2021-123956 000150974 041__ $$aeng 000150974 100__ $$0(orcid)0000-0001-9211-4475$$aGarcía-Lirola, L.C.$$uUniversidad de Zaragoza 000150974 245__ $$aUniformly convex renormings and generalized cotypes 000150974 260__ $$c2021 000150974 5060_ $$aAccess copy available to the general public$$fUnrestricted 000150974 5203_ $$aWe 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. 000150974 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/ MTM2017-83262-C2-2-P 000150974 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000150974 590__ $$a1.675$$b2021 000150974 591__ $$aMATHEMATICS$$b59 / 333 = 0.177$$c2021$$dQ1$$eT1 000150974 592__ $$a1.935$$b2021 000150974 593__ $$aMathematics (miscellaneous)$$c2021$$dQ1 000150974 594__ $$a2.6$$b2021 000150974 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000150974 700__ $$aRaja, M. 000150974 7102_ $$12006$$2015$$aUniversidad de Zaragoza$$bDpto. Matemáticas$$cÁrea Análisis Matemático 000150974 773__ $$g383 (2021), 107679 [23 pp.]$$pAdv. math.$$tAdvances in Mathematics$$x0001-8708 000150974 8564_ $$s447788$$uhttps://zaguan.unizar.es/record/150974/files/texto_completo.pdf$$yVersión publicada 000150974 8564_ $$s1265601$$uhttps://zaguan.unizar.es/record/150974/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000150974 909CO $$ooai:zaguan.unizar.es:150974$$particulos$$pdriver 000150974 951__ $$a2025-02-21-09:51:36 000150974 980__ $$aARTICLE