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Dissipative operators and additive perturbations in locally convex spaces
Author(s) -
Albanese Angela A.,
Jornet David
Publication year - 2016
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500150
Subject(s) - mathematics , dissipative system , dissipative operator , banach space , ergodic theory , pure mathematics , semigroup , function space , perturbation (astronomy) , regular polygon , operator (biology) , convex function , hilbert space , mathematical analysis , geometry , physics , biochemistry , chemistry , repressor , quantum mechanics , transcription factor , gene
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 andrg ( λ I − A ) ⊆ X is dense in X for some λ > 0 . 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.