Abstract and Applied Analysis
Volume 5 (2000), Issue 4, Pages 227-244

A new characterization of B-bounded semigroups with application to implicit evolution equations

Luisa Arlotti

Dipartimento di Ingegneria Civile, via delle Scienze, Udine 208 33100, Italy

Received 22 September 2000

Copyright © 2000 Luisa Arlotti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and called B-bounded semigroups. We first determine all the properties possessed by a couple (A,B) of operators if they generate a B-bounded semigroup (Y(t))t0. Then we determine the simplest further property of the couple (A,B) which can assure the existence of a C0-semigroup (T(t))t0 such that for all t0,fD(B) we can write Y(t)f=T(t)Bf. 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.