Some more twisted Hilbert spaces


  • Daniel Morales Universidad de Extremadura, Departamento de Matemáticas
  • Jesús Suárez de la Fuente Universidad de Extremadura, Departamento de Matemáticas


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