A new characterization of B-bounded semigroups with application to implicit evolution equations. (2000) - Arlotti, Luisa
Abstract : We consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and calledB -bounded semigroups. We first determine all the properties possessed by a couple( A, B ) of operators if they generate aB -bounded semigroup( Y ( t ) ) t ≥ 0 . Then we determine the simplest further property of the couple( A, B ) which can assure the existence of aC 0 -semigroup( T ( t ) ) t ≥ 0 such that for allt ≥ 0, f ∈ D ( B ) we can writeY ( t ) f = T ( t ) B f . Furthermore, we compare our result with the previous ones and finally we show how our method allows to improve the theory developed by Banasiak for solving implicit evolution equations.