Luisa Arlotti, "A new characterization of -bounded semigroups with application to implicit evolution equations", Abstract and Applied Analysis, vol. 5, Article ID 507567, 18 pages, 2000. https://doi.org/10.1155/S1085337501000331
A new characterization of -bounded semigroups with application to implicit evolution equations
We consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and called -bounded semigroups. We first determine all the properties possessed by a couple of operators if they generate a -bounded semigroup . Then we determine the simplest further property of the couple which can assure the existence of a -semigroup such that for all we can write . 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.
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