EMIS ELibM Electronic Journals Zeitschrift für Analysis und ihre Anwendungen
Vol. 19, No. 1, pp. 23-34 (2000)

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On $B$-Bounded Semigroups as a Generalization of $C_0$-Semigroups

L. Arlotti

Dipartimento di Ingegneria Civile, via delle Scienze 208, 33100 Udine, Italy

Abstract: In 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.

Classification (MSC2000): 47D06

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Electronic fulltext finalized on: 25 Jul 2001. This page was last modified: 9 Nov 2001.

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