Israel Journal of Mathematics

, Volume 81, Issue 1–2, pp 227–255 | Cite as

C-semigroups and strongly continuous semigroups

  • Ralph deLaubenfels


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 −1 x‖. 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.


Banach Space Mild Solution Fractional Power Continuous Semigroup Interpolation Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Hebrew University 1993

Authors and Affiliations

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

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