Strongly Continuous Semigroups on Some Fréchet Spaces

@inproceedings{Jord2015StronglyCS,
  title={Strongly Continuous Semigroups on Some Fréchet Spaces},
  author={Enrique Rubio Jord{\`a} and Thomas Kalmes and JOCHEN WENGENROTH},
  year={2015}
}
We prove that for a strongly continuous semigroup T on the Fréchet space ω of all scalar sequences, its generator is a continuous linear operator A ∈ L(ω) and that, for all x ∈ ω and t ≥ 0, the series exp(tA)(x) = ∞ ∑ k=0 t k! Ak(x) converges to Tt(x). This solves a problem posed by Conejero. Moreover, we improve recent results of Albanese, Bonet, and Ricker about semigroups on strict projective limits of Banach spaces. 

From This Paper

Topics from this paper.

References

Publications referenced by this paper.
Showing 1-8 of 8 references

Hypercyclic and mixing operator semigroups

Stanislav Shkarin
Proc. Edinb. Math. Soc. (2) • 2011

C0-semigroups and mean ergodic operators in a class of Fréchet spaces

Angela A. Albanese, José Bonet, Werner J. Ricker
J. Math. Anal. Appl • 2010

Ricker , C 0 - semigroups and mean ergodic operators in a class of Fréchet spaces

José Bonet Angela A. Albanese, J Werner
J . Math . Anal . Appl . • 2010

Conejero , On the existence of transitive and topologically mixing semigroups

A José
Bull . Belg . Math . Soc . Simon Stevin • 2007

On the existence of transitive and topologically mixing semigroups

José A. Conejero
Bull. Belg. Math. Soc. Simon Stevin • 2007

Band 123

Kôsaku Yosida, Functional analysis, Die Grundlehren der Mathematischen Wissenschaften
Academic Press Inc., New York, • 1965

Semi - groups of operators in locally convex spaces

Hikosaburo Komatsu
J . Math . Soc . Japan • 1964

Similar Papers

Loading similar papers…