Operator semigroups in Banach space theory

Aiena, Pietro; González, Manuel; Martínez-Abejón, Antonio

Aiena, Pietro ; González, Manuel ; Martínez-Abejón, Antonio

Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001), p. 157-205 / Harvested from Biblioteca Digitale Italiana di Matematica

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Résumé

In questo lavoro, motivati dalla teoria di Fredholm in spazi di Banach e dalla cosiddetta teoria degli ideali di operatori nel senso di Pietsch, viene definito un nuovo concetto di semigruppo di operatori. Questa nuova definizione include quella di molte classi di operatori già studiate in letteratura, come la classe degli operatori di semi-Fredholm, quella degli operatori tauberiani ed altre ancora. Inoltre permette un nuovo ed unificante approccio ad una serie di problemi in teoria degli operatori su spazi di Banach. Ad un ideale di operatori $A$ vengono associati, in modo naturale, due semigruppi di operatori $A_{+}$ e $A_{-}$ . In particolare, se $W$ è la classe degli operatori debolmente compatti, il semigruppo di operatori associato $W_{+}$ è la classe degli operatori tauberiani. Questo lavoro contiene, oltre che una panoramica sulle proprietá, gli esempi e le applicazioni di tali semigruppi, diversi nuovi risultati. Vengono inoltre posti in evidenza una serie di nuovi problemi aperti che meritano di essere studiati

Publié le : 2001-02-01

MR 1821404 | Zbl 1072.47037

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     author = {Pietro Aiena and Manuel Gonz\'alez and Antonio Mart\'\i nez-Abej\'on},
     title = {Operator semigroups in Banach space theory},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {4-A},
     year = {2001},
     pages = {157-205},
     zbl = {1072.47037},
     mrnumber = {1821404},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2001_8_4B_1_157_0}
}

Aiena, Pietro; González, Manuel; Martínez-Abejón, Antonio. Operator semigroups in Banach space theory. Bollettino dell'Unione Matematica Italiana, Tome 4-A (2001) pp. 157-205. http://gdmltest.u-ga.fr/item/BUMI_2001_8_4B_1_157_0/

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