论文标题
更多扭曲的希尔伯特空间
Some more twisted Hilbert spaces
论文作者
论文摘要
我们通过考虑与希尔伯特“接近”的特性，为扭曲的希尔伯特空间提供了三个新的例子。我们表示他们$ z（\ Mathcal J）$，$ z（\ Mathcal s^2）$和$ z（\ Mathcal t_s^2）$。第一个空间是渐近的希尔伯特人，但不是弱的希尔伯特。在另一侧，$ z（\ Mathcal S^2）$和$ z（\ Mathcal t_s^2）$不是渐近的希尔伯特式。此外，空间$ z（\ mathcal t_s^2）$是一个快乐的空间，证明它给出了约翰逊和szankowski定理的“扭曲”版本（Ann。Math。176：1987--2001，2012）。这是，我们可以构建一个非平凡的扭曲希尔伯特空间，以便从$ n $维的子空间到$ \ ell_2^n $的同构常数像我们希望$ n \ \ n \ \ \ infty $一样慢。
We provide three new examples of twisted Hilbert spaces by considering properties that are "close" to Hilbert. We denote them $Z(\mathcal J)$, $Z(\mathcal S^2)$ and $Z(\mathcal T_s^2)$. The first space is asymptotically Hilbertian but not weak Hilbert. On the opposite side, $Z(\mathcal S^2)$ and $Z(\mathcal T_s^2)$ are not asymptotically Hilbertian. Moreover, the space $Z(\mathcal T_s^2)$ is a HAPpy space and the technique to prove it gives a "twisted" version of a theorem of Johnson and Szankowski (Ann. of Math. 176:1987--2001, 2012). This is, we can construct a nontrivial twisted Hilbert space such that the isomorphism constant from its $n$-dimensional subspaces to $\ell_2^n$ grows to infinity as slowly as we wish when $n\to \infty$.
