In this paper an automorphism of a unital C-algebra is said to be locally inner if on any element it agrees with some inner automorphism. We make a fairly complete study of local innerness in von Neumann algebras, incorporating comparison with the pointwise innerness of Haagerup-Størmer. On some von Neumann algebras, including all with separable predual, a locally inner automorphism must be inn...

One of the most important auxiliary objects associated with an operator algebra is its state space. The two books under review describe the authors’ solutions, obtained together with H. Hanche-Olsen and B. Iochum [1], [2], [9], to the problems: What data must be added to a state space so that the operator algebra can be recovered? and Which convex sets can arise as state spaces? As that work is...