A remark on exponentially bounded C-semigroups. (English) Zbl 0731.47040

Miyadera, Isao; Tanaka, Naoki

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)

MSC:

47B48	Linear operators on Banach algebras
47D06	One-parameter semigroups and linear evolution equations

Keywords:

representation theory; generation of semigroups; abstract Cauchy problem