OpenAI research collection · 1 manuscript · Source checked 2026-10-19
Proves that every type II_(1) 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 P\subset M of such factors, the unitaries u with M=W^*(P,u) form a dense G_(δ) subset in the trace 2-norm topology.
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We prove that every type II_(1) 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.
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