Abstract
The aim of this paper is to prove that the uniform exponential stability of a strongly continuous semigroup fT(t)gt�0 (acting on a complex Hilbert space H) can be derived as a con- sequence of the well behavior of its numerical range in a suitable Orlicz space. More precisely, assuming that there exists an Orlicz space E = (L � ;� � ) over R+ such that liminf �#0 (�jjexpjjE?) = 0 and sup jjxjj�1 � � (jhT(�)x;xij) � M < 1; then the uniform growth bound !0 of the semigroup veri…es an estimate of the form !0 � M� := � (2MjjexpjjE?) 1 < 0 for some positive number �: As an application, the well posedness of an abstract in…nite time Cauchy problem is discussed.
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