Maximal amenable MASAs of radial type in the free group factors

We prove that if { ( M j , τ j ) } j ∈ J \{(M_j, \tau _j)\}_{j\in J} are tracial von Neumann algebras, s j ∈ M j s_j \in M_j are selfadjoint semicircular elements and t = ( t j ) j t=(t_j)_j is a square summable J J -tuple of real numbers with at least two non-zero entries, then the von Neumann algebra A ( t ) A(t) generated by the “weighted radial element” ∑ j t j s j ∈ M ≔ ∗ j ∈ J M j \sum _j t_j s_j\in M≔*_{j\in J} M_j is maximal amenable in M M , with A ( t ) A(t) , A ( t ′ ) A(t’)