Universality, complexity and asymptotically uniformly smooth Banach spaces

Ryan M. Causey; Gilles Lancien

Commentationes Mathematicae Universitatis Carolinae (2023)

  • Volume: 64, Issue: 1, page 1-17
  • ISSN: 0010-2628

Abstract

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For 1 < p ≤ ∞ , 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 = ∞ .

How to cite

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Causey, Ryan M., and Lancien, Gilles. "Universality, complexity and asymptotically uniformly smooth Banach spaces." Commentationes Mathematicae Universitatis Carolinae 64.1 (2023): 1-17. <http://eudml.org/doc/299439>.

@article{Causey2023,
abstract = {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 $.},
author = {Causey, Ryan M., Lancien, Gilles},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {asymptotic smoothness in Banach space; universality; complexity},
language = {eng},
number = {1},
pages = {1-17},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Universality, complexity and asymptotically uniformly smooth Banach spaces},
url = {http://eudml.org/doc/299439},
volume = {64},
year = {2023},
}

TY - JOUR
AU - Causey, Ryan M.
AU - Lancien, Gilles
TI - Universality, complexity and asymptotically uniformly smooth Banach spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2023
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 64
IS - 1
SP - 1
EP - 17
AB - 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 $.
LA - eng
KW - asymptotic smoothness in Banach space; universality; complexity
UR - http://eudml.org/doc/299439
ER -

References

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