通用性、复杂性与渐近一致光滑Banach空间

IF 0.2 Q4 MATHEMATICS

Commentationes Mathematicae Universitatis Carolinae Pub Date : 2023-11-13 DOI:10.14712/1213-7243.2023.015

R Causey, Gilles Lancien

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引用次数: 1

摘要

对于$1 < p \le \infty$，我们证明了具有等价的$p$ -渐近一致光滑范数的所有可分Banach空间类的单射和满射泛的Banach空间的存在性。在可分离巴拿赫空间中证明了该类是解析完备的。这些结果扩展了N. J. Kalton, D. Werner和O. Kurka在$p=\infty$案例中的先前工作。

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Universality, complexity and asymptotically uniformly smooth Banach spaces

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 $p=\infty$.

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来源期刊

Commentationes Mathematicae Universitatis Carolinae MATHEMATICS-

CiteScore

0.60

自引率

0.00%

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