Ultraweakly compact operators and dual spaces

Alvarez, Teresa

Alvarez, Teresa

Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004), p. 697-711 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

In this paper, the class of all bounded ultraweakly compact operators in Banach spaces is introduced and characterised in terms of their first and second conjugates. We analize the relationship between an ultraweakly compact operator and its conjugate. Examples of operators belonging to this class are exhibited. We also investigate the connection between ultraweak compactness of $T \in L (X, Y)$ and minimal subspaces of $Y^{'}$ and we present a result of factorisation for ultraweakly compact operators.

In questo articolo si introduce e si caratterizza la classe di tutti gli operatori ultradebolmente compatti, definiti negli spazi di Banach per mezzo dei loro operatori coniugati. Si analizza la relazione esistente fra un operatore ultradebolmente compatti e il suo coniugato. Si presentano esempi di operatori appartenenti a questa classe. Inoltre, si studia la connessione fra la compattezza ultradebole di $T \in L (X, Y)$ e i sottospazi minimali di $Y^{'}$ e si presenta un risultato relativo alla fattorizzazione degli operatori ultradebolmente compatti.

Publié le : 2004-10-01

MR 2101660 | Zbl 1179.47020

@article{BUMI_2004_8_7B_3_697_0,
     author = {Teresa Alvarez},
     title = {Ultraweakly compact operators and dual spaces},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {7-A},
     year = {2004},
     pages = {697-711},
     zbl = {1179.47020},
     mrnumber = {2101660},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_3_697_0}
}

Alvarez, Teresa. Ultraweakly compact operators and dual spaces. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 697-711. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_3_697_0/

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