Zeitschrift für Analysis und ihre Anwendungen
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Published online: 2000-03-31
On $B$-Bounded Semigroups as a Generalization of $C_0$-SemigroupsLuisa Arlotti (1) Università di Udine, Italy
this paper we consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and called $B$-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 ($A, B$) of linear operators be the generator of a $B$-bounded semigroup. Our procedure is constructive and is equivalent to the Yosida procedure for the construction of a $C_0$-semigroup when $B = I$. We also show that our result represents a generalization of Banasiak’s result.
Keywords: $B$-bounded semigroups, $C_0$-semigroups
Arlotti Luisa: On $B$-Bounded Semigroups as a Generalization of $C_0$-Semigroups. Z. Anal. Anwend. 19 (2000), 23-34. doi: 10.4171/ZAA/936