Type III factors: central sequences, full factors and almost periodic states

This course studies factors of type III through bounded sequences that asymptotically commute with the whole algebra and its normal states. It shows that a factor with separable predual is full, meaning that its inner automorphisms form a closed subgroup, exactly when all such sequences are trivial; it builds the invariants Sd and τ from almost periodic weights and the modular group; and it constructs full factors of type III₁ that have no almost periodic weight and are not crossed products of a semifinite algebra by a discrete abelian group. Basic references are [Connes 1974], [Connes 1973], [Connes 1976] and [Takesaki II].

1. Ultraproducts and the asymptotic centralizer
2. Full factors
3. Almost periodic weights and the invariant \(Sd\)
4. Full factors without almost periodic weights

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