Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4308
 Title: Lectures on Rosenthal's l^1-theorem Authors: Behrends, Ehrhard Issue Date: 2000 Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche Source: Ehrhard Behrends, "Lectures on Rosenthal's l^1-theorem", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 31 (2000) suppl.1, pp. 71-106. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics31 (2000) suppl.1 Abstract: Let $x\left(n\right)$ be a bounded sequence in a Banach space X.Rosenthal's $l^{1}$-theorem states that there is essentially onlyone exceptional situation where it is $\mathit{not}$ possible toextract a subsequence which is a weak Cauchy sequence: This happensif (x$_{n}$) is the sequence of unit vectors in $l^{1}$.The aimof these lectures is twofold: On the one hand results from the lastfew years centering around this theorem are presented, and on theother hand the opportunity is taken to introduce the audience to anumber of techniques which are of importance in modern Banach spacetheory (Ramsey theory, Martin's axiom, ... ). Type: Article URI: http://hdl.handle.net/10077/4308 ISSN: 0049-4704 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.31 (2000) s1

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