Miyadera, Isao; Tanaka, Naoki A remark on exponentially bounded C-semigroups. (English) Zbl 0731.47040 Proc. Japan Acad., Ser. A 66, No. 2, 31-34 (1990). The main purpose of this note is to prove the equivalence of two statements. (1) A is the generator of a special type of semigroup on a Banach space X. (2) A satisfies certain properties on sets included in X. Applications are given in representation theory, in the generation of semigroups and on the abstract Cauchy problem. Reviewer: B.Burrows (Stafford) Cited in 1 ReviewCited in 6 Documents MSC: 47B48 Linear operators on Banach algebras 47D06 One-parameter semigroups and linear evolution equations Keywords:representation theory; generation of semigroups; abstract Cauchy problem PDF BibTeX XML Cite \textit{I. Miyadera} and \textit{N. Tanaka}, Proc. Japan Acad., Ser. A 66, No. 2, 31--34 (1990; Zbl 0731.47040) Full Text: DOI