New examples of weak Hilbert spaces

We prove that the Rochberg spaces \(\mathsf R_{1/2}^{(n)}(\textsf{T}_2)\) ${\mathsf{R}}_{1/2}^{(n)}({\mathsf{T}}_2)$ associated to the complex interpolation pair \((\textsf{T}_2,\textsf{T}_2^*)\) $({\mathsf{T}}_2,{\mathsf{T}}_2^{\ast })$ , defined by the 2-convexification of the Tsirelson space and its dual, are weak Hilbert spaces. This generalizes the results obtained in Suárez de la Fuente (J Inst Math Jussieu 19:855–867, 2020).