Mean stability of semigroups. (Q1607721)

The authors consider the concept of mean stability of a bounded \(C_0\)-semigroup \(T(.)\) with respect to a suitable family of weight functions. For instance, it is shown that the infinitesimal generator \(A\) of \(T(.)\) has dense range if and only if \(T(.)\) is mean stable for all appropriate weights. Moreover, they show that analogous results are valid for power bounded operators, tensor product semigroups and cosine operator functions.