Abelian Subalgebras of Von Neumann Algebras

a e G abelian in G abelian von Neumann algebra G automorphic hull automorphically normal automorphically thick automorphism of G c(Pi completes the proof contraction of G Corollary countable define Definition denote dimension function equivalent ergodic example exist projections exists a family F a projection f e H factor G factor of type faithful normal full 7-group G is finite G of type Hilbert space hyperfinite factor induces a e inner automorphisms isomorphism multiplicity function Neumann algebra Neumann subalgebra non-zero projection normal contraction normal G-trace normal in G o e G orthogonal projections orthonormal basis p-adic partial isometry positive integer projection F projection of G proposition 4.3 Radon–Nikodym theorem real number strongly finite subalgebra of G subset substantial in G Suppose that G supremum theorem 9.2 thick in G type II1 ultraweak topology uniform multiplicity unitary operators Zorn's lemma