Family 296Operator algebrasLeanNot yet digested
The generator problem for finite factors
Proves that every type II factor with separable predual is generated by a single operator, equivalently by two self-adjoint operators, resolving the generator problem. More strongly, for every irreducible inclusion of such factors, the unitaries u with form a dense G subset in the trace 2-norm topology.
Manuscripts in this family · 1
Relative generation and the generator problem for finite factors
Sep 23, 2026·paper.pdfLean
We prove that every type II factor with separable predual is generated by one operator, equivalently by two self-adjoint operators. Combined with the established direct-integral reduction to this case, this gives an affirmative solution of the generator problem for von Neumann algebras with separable predual.