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

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  • Luisa Arlotti

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.

Suggested Citation

  • Luisa Arlotti, 2000. "A new characterization of B -bounded semigroups with application to implicit evolution equations," Abstract and Applied Analysis, Hindawi, vol. 5, pages 1-18, January.
    • Handle: RePEc:hin:jnlaaa:507567
    DOI: 10.1155/S1085337501000331
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