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