×

zbMATH — the first resource for mathematics

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

MSC:
47B48 Linear operators on Banach algebras
47D06 One-parameter semigroups and linear evolution equations
PDF BibTeX XML Cite
Full Text: DOI