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arXiv · 1309.4946

Strongly continuous semigroups on some Fr\'echet spaces

Leonhrd Frerick·Enrique Jordá·Thomas Kalmes·Jochen Wengenroth
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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.

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Leonhrd Frerick, Enrique Jordá, Thomas Kalmes, Jochen Wengenroth. 2013-09-19. Strongly continuous semigroups on some Fr\'echet spaces. https://arxiv.org/abs/1309.4946

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