Balanced Exponential Growth of Operator Semigroups

A C0-semigroup S t., tG0, on a Banach space X weakly, strongly, uniformly. approaches balanced or asynchronous.exponential growth if there exists some sgR such that Ps lim eys tS t. tª` exists in the weak, strong, uniform operator topology.and P is not the 0 operator. In this paper, the strong and uniform approach to balanced exponential growth is characterized and applicable sufficient conditions are derived. The results will be applied to models for age-size-structured population dynamics in a forthcoming publication.