On -Bounded Semigroups as a Generalization of -Semigroups
Luisa Arlotti
Università di Udine, Italy
![On $B$-Bounded Semigroups as a Generalization of $C_0$-Semigroups cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-zaa-volume-19-issue-1.png&w=3840&q=90)
Abstract
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. 23–34
DOI 10.4171/ZAA/936