JournalszaaVol. 19, No. 1pp. 23–34

On BB-Bounded Semigroups as a Generalization of C0C_0-Semigroups

  • Luisa Arlotti

    Università di Udine, Italy
On $B$-Bounded Semigroups as a Generalization of $C_0$-Semigroups cover
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this paper we consider the one-parameter family of linear operators that A. Belleni Morante recently introduced and called BB-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,BA, B) of linear operators be the generator of a BB-bounded semigroup. Our procedure is constructive and is equivalent to the Yosida procedure for the construction of a C0C_0-semigroup when B=IB = I. We also show that our result represents a generalization of Banasiak’s result.

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Luisa Arlotti, On BB-Bounded Semigroups as a Generalization of C0C_0-Semigroups. Z. Anal. Anwend. 19 (2000), no. 1, pp. 23–34

DOI 10.4171/ZAA/936