English

Strongly continuous semigroups on some Fr\'echet spaces

Functional Analysis 2013-09-23 v2

Abstract

We prove that for a strongly continuous semigroup on the Fr\'echet space of all scalar sequences, its generator is a continuous linear operator and that the semigroup can be represented as exp(tA) where the exponential series converges in a very strong sense. 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.

Keywords

Cite

@article{arxiv.1309.4946,
  title  = {Strongly continuous semigroups on some Fr\'echet spaces},
  author = {Leonhrd Frerick and Enrique Jordá and Thomas Kalmes and Jochen Wengenroth},
  journal= {arXiv preprint arXiv:1309.4946},
  year   = {2013}
}

Comments

6 pages

R2 v1 2026-06-22T01:30:12.333Z