Geodesic
Universality, complexity and asymptotically uniformly smooth Banach spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 1, pp. 1-17.

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For $1 p \le \infty$, we show the existence of a Banach space which is both injectively and surjectively universal for the class of all separable Banach spaces with an equivalent $p$-asymptotically uniformly smooth norm. We prove that this class is analytic complete in the class of separable Banach spaces. These results extend previous works by N. J. Kalton, D. Werner and O. Kurka in the case $p=\infty$.
DOI : 10.14712/1213-7243.2023.015
Classification : 46B03, 46B06, 46B20
Keywords: asymptotic smoothness in Banach space; universality; complexity 
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Causey, Ryan M.; Lancien, Gilles. Universality, complexity and   asymptotically uniformly smooth Banach spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 1, pp. 1-17. doi : 10.14712/1213-7243.2023.015. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2023.015/

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