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 $\mathcal{A}$ vengono associati, in modo naturale, due semigruppi di operatori $\mathcal{A}_{+}$ e $\mathcal{A}_{-}$. 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
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Con il contributo del Ministero per i Beni e le Attività Culturali