The separable case of Kadison's problem on orthonormal bases of unitaries for type ${\mathrm{II}}_1$ factors

Yixin He, Quanyu Tang, Teng Zhang

In 1967, Kadison asked ``does every type ${\mathrm{II}}_1$ factor have an orthonormal (with respect to the trace) basis consisting of unitaries?'' Using a noncommutative Lyapunov the…