Relative generation and the generator problem for finite factors
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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A single generation theorem for simple unital $C^*$-algebras with CPoU and comparisonarXiv.orgXin MaOct 20, 2026in the index
In this note, assuming the finite factor generation theorem obtained by OpenAI, we demonstrate that if a separable simple unital $C^*$-algebra $A$ with nonempty trace space, has the strict comparison for positive elements, and its uniform tracial completion has complemented partitions of unity…