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Holomorphic C-semigroups and holomorphic semigroups. (English) Zbl 0651.47028
This paper is concerned with holomorphic C-semigroups. The main purpose is to give a characterization of the C-complete infinitesimal generator of a holomorphic C-semigroup, which coincides with that of a holomorphic \((C_ 0)\)-semigroup in the case of \(C=I\). We also clarify the relationship between holomorphic C-semigroups and holomorphic semigroups of growth order \(\alpha\). Applying the theory for holomorphic C- semigroups, we deduce a characterization of the complete infinitesimal generator of a holomorphic semigroup of growth order \(\alpha\).
Reviewer: N.Tanaka

47D03 Groups and semigroups of linear operators
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