  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-Stormer. On some von
Neumann algebras, including all with separable predual, a locally inner
automorphism must be inner. But a transfinitely recursive construction
demonstrates that this is not true in general. As an application, we show that
the diagonal sum descends to a well-defined map on the automorphism orbits of a
unital C*-algebra if and only if all its automorphisms are locally inner.
