Rosenthal and semi-Tauberian linear relations in normed spaces

Álvarez, Teresa ; Martínez-Abejón, Antonio

Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 3, pp. 707-722.

Abstract (VO)

The class of Rosenthal linear relations in normed spaces is introduced and studied in terms of their first and second conjugates. We investigate the relationship between a Rosenthal linear relation and its conjugate. In this paper, we also study the semi-Tauberian linear relations following the pattern followed for the study of the Tauberian linear relations. We prove that the semi-Tauberian linear relations share some of the properties of Tauberian linear relations and they are related to Rosenthal linear relations in the same way as Tauberian linear relations are related to weakly compact linear relations. We describe examples and investigate special cases: in particular, $F_{+}$ and strictly singular linear relations.

Riassunto

Si introduce la classe delle relazioni lineari di Rosenthal in spazi normati e si studia in termini dei suoi coniugati primi e secondi. Si analizza il rapporto fra una relazione lineare di Rosenthal e il suo coniugato. Nell'articolo si studiano inoltre le relazioni lineari semi-Tauberiane che seguono il modello adottato nello studio delle relazioni lineari Tauberiane. Si dimostra che le relazioni lineari semi-Tauberiane condividono alcune delle proprietà delle relazioni lineari Tauberiane e che stanno in relazione alle relazioni lineari di Rosenthal nello stesso modo in cui le relazioni lineari Tauberiane si trovano in relazione con le relazioni lineari debolmente com- patte. Si descrivono esempi e si discutono casi particolari, $F_{+}$ e le relazioni lineari strettamente singolari.

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