Dissipative operators and additive perturbations in locally convex spaces |
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| Authors: | Angela A Albanese David Jornet |
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| Affiliation: | 1. Dipartimento di Matematica e Fisica “E. De Giorgi”, Università del Salento, Via per Arnesano, Lecce, Italy;2. Instituto Universitario de Matemática Pura y Aplicada IUMPA, Universitat Politècnica de València, Valencia, Spain |
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| Abstract: | Let  be a densely defined operator on a Banach space X. Characterizations of when  generates a C0‐semigroup on X are known. The famous result of Lumer and Phillips states that it is so if and only if  is dissipative and  is dense in X for some  . There exists also a rich amount of Banach space results concerning perturbations of dissipative operators. In a recent paper Tyran–Kamińska 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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| Keywords: | Equicontinuous semigroup dissipative operator additive perturbation (uniformly) mean ergodic operator quasi‐Montel operator locally convex space Primary: 47B44 47A55 46A99 Secondary: 47D03 47A35 |
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