Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418543 | Journal of Mathematical Analysis and Applications | 2014 | 4 Pages |
Abstract
We prove that for a strongly continuous semigroup T on the Fréchet space Ï of all scalar sequences, its generator is a continuous linear operator AâL(Ï) and that, for all xâÏ and t⩾0, the series exp(tA)(x)=âk=0âtkk!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.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Leonhard Frerick, Enrique Jordá, Thomas Kalmes, Jochen Wengenroth,