Geodesic
Some more twisted Hilbert spaces
Daniel Morales1 ; Jesús Suárez de la Fuente1
1 Universidad de Extremadura, Departamento de Matemáticas
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 819-837

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  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

Daniel Morales 1 ; Jesús Suárez de la Fuente 1

1 Universidad de Extremadura, Departamento de Matemáticas 
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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/