论文标题
Banach空间中的渐近平滑度和普遍性
Asymptotic smoothness and universality in Banach spaces
论文作者
论文摘要
对于$ 1 <p \ leqslant \ infty $，我们研究了两类可分开的Banach空间的复杂性和通用空间，表示为$ \ textsf {a} _p $和$ \ textsf {n} _p $，以及与Banach空间中的渐近平滑度相关的。我们表明，这些类别中的每一个都是可分开的Banach空间类中的Borel。然后，我们建立了小型的Banach空间家庭，这些空间既是这些班级的均匀且过时的普遍性。最后，我们通过尤其证明这些阶级都无法接受通用空间，从而证明了这种普遍性结果的最佳性。
For $1<p\leqslant \infty$, we study the complexity and the existence of universal spaces for two classes of separable Banach spaces, denoted $\textsf{A}_p$ and $\textsf{N}_p$, and related to asymptotic smoothness in Banach spaces. We show that each of these classes is Borel in the class of separable Banach spaces. Then we build small families of Banach spaces that are both injectively and surjectively universal for these classes. Finally, we prove the optimality of this universality result, by proving in particular that none of these classes admits a universal space.
