Gonzalo, R.Jaramillo Aguado, Jesús ÁngelYáñez, Javier2023-06-172023-06-1720170944-6532https://hdl.handle.net/20.500.14352/17909The following articles are so far only available in electronic form. The printed version will be published in December 2017.We introduce a suitable notion of asymptotic smoothness on infinite dimensional Banach spaces, and we prove that, under some structural restrictions on the space, the convex envelope of an asymptotically smooth function is asymptotically smooth. Furthermore, we study convexity and smoothness properties of polynomial norms, and we obtain that a polynomial norm of degree N has modulus of convexity of power type N.engjournal articlehttp://www.heldermann.de/JCA/JCA24/JCA244/jca24073.htmhttp://www.heldermann.de/open access517.98Análisis funcional y teoría de operadores