On the positivity of semigroups of operators
Lemmert, Roland ; Volkmann, Peter
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 483-489 / Harvested from Czech Digital Mathematics Library
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In a Banach space $E$, let $U(t)$ $\,(t>0)$ be a $C_0$-semigroup with generating operator $A$. For a cone $K\subseteq E$ with non-empty interior we show: $(\star)$ \quad $U(t)[K]\subseteq K$ $\,(t>0)$ holds if and only if $A$ is quasimonotone increasing with respect to $K$. On the other hand, if $A$ is not continuous, then there exists a regular cone $K\subseteq E$ such that $A$ is quasimonotone increasing, but $(\star)$ does not hold.

Publié le : 1998-01-01
Classification:  47B65,  47D06 
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     author = {Roland Lemmert and Peter Volkmann},
     title = {On the positivity of semigroups of operators},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {483-489},
     zbl = {0970.47026},
     mrnumber = {1666770},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119026}
}

Lemmert, Roland; Volkmann, Peter. On the positivity of semigroups of operators. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 483-489. http://gdmltest.u-ga.fr/item/119026/

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