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      The growth bound for strongly continuous semigroups on Fr\'echet spaces

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          Abstract

          We introduce the concepts of growth and spectral bound for strongly continuous semigroups acting on Fr\'echet spaces and show that the Banach space inequality \(s(A)\leqslant\omega_0(T)\) extends to the new setting. Via a concrete example of an even uniformly continuous semigroup we illustrate that for Fr\'echet spaces effects with respect to these bounds may happen that cannot occur on a Banach space.

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          A Spectral Theory for Locally Convex Algebras

           G. Allan (1965)
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            Semigroups of operators in locally convex spaces

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              Strongly continuous semigroups on some Fréchet spaces

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                Author and article information

                Journal
                2014-08-21
                Article
                10.1017/S0013091515000310
                1408.5037

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                Primary 47D06, Secondary 46A04, 34G10
                Proc. Edinb. Math. Soc. (2016) 59, no. 3, 801-810
                6 pages
                math.FA

                Functional analysis

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