Unbounded derivations ofC*-algebras II

It is demonstrated that a closed symmetric derivation δ of aC?-algebra (mathfrak{A}) generates a strongly continuous one-parameter group of automorphisms of aC?-algebra (mathfrak{A}) if and only if, it satisfies one of the following three conditions

1. (αδ+1)(D(δ))= (mathfrak{A}) , α∈?{0}.
2. δ possesses a dense set of analytic elements.
3. δ possesses a dense set of geometric elements.

Together with one of the following two conditions

1. ∥(αδ+1)(A)∥≧∥A∥, α∈IR,A∈D(δ).
2. If α∈IR andA∈D(δ) then (αδ+1)(A)≧0 impliesA≧0.

Other characterizations are given in terms of invariant states and the invariance ofD(δ) under the square root operation of positive elements.