Let δ be the generator of a
C0-group of *-automorphisms of a
C*-algebra \mathcal{A} and
H a differential operator of the form
H=∑\limits
m=0p λ
mδ
m,
where λ
m∈
C. It is known from a previous work that if \mathcal{A} is abelian then
H is a dissipation, i. e.
H(
a*a){≤}
a*H(
a)+
H(
a*)
a,
a∈
D(
H),
if, and only if, λ
m=0 for
m>2, λ
2{≤}0, and λ
0{≥}0. This conclusion is no longer generally true for non-abelian \mathcal{A}, but it is true in a variety of special cases which we discuss, e. g. if \mathcal{A} is isomorphic to the
C*-algebra of all compact operators on a Hilbert space \mathcal{H} and σ is unbounded.
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