This is the abstract of the paper
  "Operator theoretic properties of semigroups in terms of their generators "
by Soenke Blunck and Lutz Weis.

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Abstract:
Let $(T_t)$ be a $C_0$ semigroup with generator $A$ on a Banach space $X$
and let ${\cal A}$ be an operator ideal, e.g. the class of compact,
Hilbert-Schmidt or trace class operators. We show that the resolvent
$R(\lambda,A)$ of $A$ belongs to ${\cal A}$ if and only if
the integrated semigroup $S_t:=\int_0^t T_s ds$ belongs to ${\cal A}$.
For analytic semigroups, $S_t\in{\cal A}$ implies $T_t\in{\cal A}$, and in
this case we give precise estimates for the growth of the ${\cal A}$-norm of
$T_t$ (e.g. the trace of $T_t$) in terms of the resolvent growth and the
imbedding $D(A) \hookrightarrow X$.

1991 Mathematics Subject Classification: 47A60 , 47B10 , 47D06

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