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

Luisa Arlotti

Abstract and Applied Analysis, 2000, vol. 5, issue 4, 227-244

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 C0‐semigroup (T(t))t≥0 such that for all t ≥ 0, f ∈ D(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.

Date: 2000
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https://doi.org/10.1155/S1085337501000331

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:5:y:2000:i:4:p:227-244

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