Some more twisted Hilbert spaces
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 819-837
Cet article a éte moissonné depuis la source Journal.fi
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 $n\to \infty$.
Keywords:
Weak Hilbert, interpolation, twisted Hilbert, centralizer
Affiliations des auteurs :
Daniel Morales 1 ; Jesús Suárez de la Fuente 1
@article{AFM_2021_46_2_a14,
author = {Daniel Morales and Jes\'us Su\'arez de la Fuente},
title = {Some more twisted {Hilbert} spaces},
journal = {Annales Fennici Mathematici},
pages = {819--837},
year = {2021},
volume = {46},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a14/}
}
Daniel Morales; Jesús Suárez de la Fuente. Some more twisted Hilbert spaces. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 819-837. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a14/