Israel Journal of Mathematics

, Volume 81, Issue 1, pp 227–255

C-semigroups and strongly continuous semigroups

  • Ralph deLaubenfels
Article

DOI: 10.1007/BF02761308

Cite this article as:
deLaubenfels, R. Israel J. Math. (1993) 81: 227. doi:10.1007/BF02761308

Abstract

We show that, whenA generates aC-semigroup, then there existsY such that [M(C)] →YX, andA|Y, the restriction ofA toY, generates a strongly continuous semigroup, where ↪ means “is continuously embedded in” and ‖x[Im(C)]≡‖C−1x‖. There also existsW such that [C(W)] →XW, and an operatorB such thatA=B|X andB generates a strongly continuous semigroup onW. If theC-semigroup is exponentially bounded, thenY andW may be chosen to be Banach spaces; in general,Y andW are Frechet spaces. If ρ(A) is nonempty, the converse is also true.

We construct fractional powers of generators of boundedC-semigroups.

Copyright information

© Hebrew University 1993

Authors and Affiliations

  • Ralph deLaubenfels
    • 1
  1. 1.Department of MathematicsOhio UniversityAthensUSA