Dissipative operators and additive perturbations in locally convex spaces

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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.

Autore Pugliese

Tutti gli autori

  • A.A. Albanese , D. Jornet

Titolo volume/Rivista

MATHEMATISCHE NACHRICHTEN

Anno di pubblicazione

2016

ISSN

0025-584X

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

Non Disponibile

0

Ultimo Aggiornamento Citazioni

28/04/2018

Settori ERC

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Codici ASJC

Non Disponibile