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Gonzalo, R. Jaramillo Aguado, Jesús Ángel Yáñez, Javier 2023-06-17T21:59:50Z 2023-06-17T21:59:50Z 2017 0944-6532 https://hdl.handle.net/20.500.14352/17909 http://www.heldermann.de/JCA/JCA24/JCA244/jca24073.htm http://www.heldermann.de/ 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. eng open access Asymptotic Smoothness, Convex Envelopes and Polynomial Norms journal article