Some more twisted Hilbert spaces
Keywords:Weak Hilbert, interpolation, twisted Hilbert, centralizer
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 \(n\to \infty\).
How to Cite
Morales, D., & Suárez de la Fuente, J. (2021). Some more twisted Hilbert spaces. Annales Fennici Mathematici, 46(2), 819–837. Retrieved from https://afm.journal.fi/article/view/110591
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