this paper we consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and called -bounded semigroups. Such a family was studied by A. Belleni Morante himself and by J. Banasiak. Here we give a necessary and sufficient condition that a pair () of linear operators be the generator of a -bounded semigroup. Our procedure is constructive and is equivalent to the Yosida procedure for the construction of a -semigroup when . We also show that our result represents a generalization of Banasiak’s result.
Cite this article
Luisa Arlotti, On -Bounded Semigroups as a Generalization of -Semigroups. Z. Anal. Anwend. 19 (2000), no. 1, pp. 23–34DOI 10.4171/ZAA/936