POINTWISE INNER AUTOMORPHISMS OF VONNEUMANN-ALGEBRAS

An automorphism α of a von Neumann algebra M is called pointwise inner if for all φ ε{lunate} M* + there is a unitary u ε{lunate} M such that φ ° α = uφu*. We analyse such automorphisms; in particular we show that if M is a factor of type IIIλ, 0 ≤ λ < 1, with separable predual, then an automorphism α is pointwise inner if and only if there are an inner automorphism γ and an extended modular automorphism \ ̄gsc ω in the sense of Connes and Takesaki, such that α = γ ° \ ̄gsc ω. © 1990.