Strongly continuous semigroups on some Fréchet spaces

Autor: Thomas Kalmes, Leonhard Frerick, Jochen Wengenroth, Enrique Jordá
Rok vydání: 2014
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Zdroj: RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
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ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2013.10.053
Popis: We prove that for a strongly continuous semigroup T on the Frechet space omega of all scalar sequences, its generator is a continuous linear operator A is an element of L(omega) and that, for all x is an element of omega and t >= 0, the series exp(tA)(x) = Sigma(infinity)(k=0) t(k)/k! A(k)(x) converges to T-t(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. (C) 2013 Elsevier Inc. All rights reserved.
The research was partially done during a stay of the fourth named author at EPSA-UPV. This visit was supported by Proyecto Prometeo 11/2013/013. The research of the first and second named authors was supported by MICINN and FEDER, Project MTM2010-15200. The research of the second named author was partially supported by Programa de Apoyo a la Investigacion y Desarrollo de la UPV PAID-06-12.
Databáze: OpenAIRE
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