Abstract
In [3]A. Bellini-Morante defined and analysed a new one-parameter family of bounded operators which he called a B-bounded semigroup. The definition was motivated by an example from the transport theory where the evolution generated by an operator A was in a certain sense controlled by another operator B. In this paper we show that a given pair (A, B) generates a B-bounded semigroup if and only if in a certain extrapolation space related to the operator B, the closure of A generates a semigroup and we also address some related topics.
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Banasiak, J. Generation results forB-bounded semigroups. Annali di Matematica pura ed applicata 175, 307–326 (1998). https://doi.org/10.1007/BF01783690
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DOI: https://doi.org/10.1007/BF01783690