  This note concerns uniform equicontinuity of families of operators on a
separable Hilbert space H, and of families of maps on B(H). It is shown that a
one parameter group of automorphisms is uniformly equicontinuous if and only if
the group of unitaries which implements it is so. A "geometrical" necessary and
sufficient condition is given for a family of operators to be uniformly
equicontinuous.
