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

Luisa Arlotti

Abstract and Applied Analysis, 2000, vol. 5, 1-18

Abstract:

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 ) ) t ≥ 0 . Then we determine the simplest further property of the couple ( A , B ) which can assure the existence of a C 0 -semigroup ( T ( t ) ) t ≥ 0 such that for all t ≥ 0 , f ∈ D ( B ) we can write Y ( 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.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:507567

DOI: 10.1155/S1085337501000331

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