[Existence et unicité de C0-semigroupe sur L∞]
Un semigroupe sous-Markovien sur L∞ n'est pas, en général, fortement continu par rapport à la topologie de norme. Nons allons introduire une nouvelle topologie sur L∞ par rapport à laquelle les semigroupes sous-Markoviens dans la litterature deviennent C0-semigroupes. Ce sera réalisé par une extension naturelle du théorème de Phillips pour semigroupe dual. Un théorème de Hille–Yosida simplifié est fourni. Cette nouvelle topologie nous permet d'introduire la notion d'unicité dans L∞ d'un prégénérateur. Nous présentons plusieurs important opérateurs dont l'unicité dans L∞ est établie.
A sub-Markov semigroup in L∞ is in general not strongly continuous with respect to the norm topology. We introduce a new topology on L∞ for which the usual sub-Markov semigroups in the literature become C0-semigroups. This is realized by a natural extension of the Phillips theorem about dual semigroup. A simplified Hille–Yosida theorem is furnished. Moreover this new topological approach will allow us to introduce the notion of L∞-uniqueness of pre-generator. We present several important pre-generators for which we can prove their L∞-uniqueness.
Accepté le :
Publié le :
Liming Wu 1, 2 ; Yiping Zhang 2
@article{CRMATH_2002__334_8_699_0,
author = {Liming Wu and Yiping Zhang},
title = {Existence and uniqueness of {\protect\emph{C}\protect\textsubscript{0}-semigroup} in {L\protect\textsuperscript{\ensuremath{\infty}}:} a new topological approach},
journal = {Comptes Rendus. Math\'ematique},
pages = {699--704},
publisher = {Elsevier},
volume = {334},
number = {8},
year = {2002},
doi = {10.1016/S1631-073X(02)02245-8},
language = {en},
}
Liming Wu; Yiping Zhang. Existence and uniqueness of C0-semigroup in L∞: a new topological approach. Comptes Rendus. Mathématique, Volume 334 (2002) no. 8, pp. 699-704. doi : 10.1016/S1631-073X(02)02245-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02245-8/
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