We show that when the (possibly unbounded) linear operator
−
A
- A
generates a bounded holomorphic semigroup of angle
θ
\theta
, and
n
(
π
/
2
−
θ
)
>
π
/
2
n\left ( {\pi /2 - \theta } \right ) > \pi /2
, then
−
A
n
- {A^n}
generates a bounded holomorphic semigroup of angle
π
/
2
−
n
(
π
/
2
−
θ
)
\pi /2 - n\left ( {\pi /2 - \theta } \right )
. When
−
A
- A
generates a bounded holomorphic semigroup of angle
π
/
2
\pi /2
, then, for all
n
n
,
−
A
n
- {A^n}
generates a bounded holomorphic semigroup of angle
π
/
2
\pi /2
.