Let $(A, D(A))$ be a densely defined operator on a Banach space $X$. Characterizations of when $(A, D(A))$ generates a $C_0$-semigroup on $X$ are known. The famous result of Lumer and Phillips states that it is so if and only if $(A, D(A))$ is dissipative and $rg(\lambda I − A) \subseteq X$ is dense in $X$ for some $\lambda>0$. There exists also a rich amount of Banach space results concerning perturbations of dissipative operators. In a recent paper Tyran–Kaminska provides perturbation criteria of dissipative operators in terms of ergodic properties. These results, and others, are shown to remain valid in the setting of general non-normable locally convex spaces. Applications of the results to concrete examples of operators on function spaces are also presented.

Dissipative operators and additive perturbations in locally convex spaces

ALBANESE, Angela Anna;
2016

Abstract

Let $(A, D(A))$ be a densely defined operator on a Banach space $X$. Characterizations of when $(A, D(A))$ generates a $C_0$-semigroup on $X$ are known. The famous result of Lumer and Phillips states that it is so if and only if $(A, D(A))$ is dissipative and $rg(\lambda I − A) \subseteq X$ is dense in $X$ for some $\lambda>0$. There exists also a rich amount of Banach space results concerning perturbations of dissipative operators. In a recent paper Tyran–Kaminska provides perturbation criteria of dissipative operators in terms of ergodic properties. These results, and others, are shown to remain valid in the setting of general non-normable locally convex spaces. Applications of the results to concrete examples of operators on function spaces are also presented.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11587/408290
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