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Asymptotic Smoothness, Convex Envelopes and Polynomial Norms

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Gonzalo, R. and Jaramillo Aguado, Jesús Ángel and Yáñez, Javier (2017) Asymptotic Smoothness, Convex Envelopes and Polynomial Norms. Journal of Convex Analysis, 24 (4). ISSN 0944-6532

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Official URL: http://www.heldermann.de/JCA/JCA24/JCA244/jca24073.htm


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Abstract

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.


Item Type:Article
Additional Information:

The following articles are so far only available in electronic form.
The printed version will be published in December 2017.

Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:43809
Deposited On:11 Jul 2017 08:12
Last Modified:11 Jul 2017 10:26

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